Research output per year
Research output per year
- 1 - 50 out of 96 results
Search results
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2024
The A∞ Condition, ε-Approximators, and Varopoulos Extensions in Uniform Domains
Bortz, S., Poggi, B. & Tolsa Domènech, X., 9 May 2024, In: Journal of Geometric Analysis. 34, 7, 53 p., 218.Research output: Contribution to journal › Article › Research › peer-review
Open Access -
2021
A proof of Carleson's ε2-conjecture
Jaye, B., Tolsa, X. & Villa, M., 1 Jul 2021, In: Annals of Mathematics. 194, 1, p. 97-161 65 p.Research output: Contribution to journal › Article › Research › peer-review
Open Access1 Citation (Scopus) -
Harmonic measure and Riesz transform in uniform and general domains
Mourgoglou, M. & Tolsa, X., 1 Jan 2021, In: Journal fur die Reine und Angewandte Mathematik. 2020, 758, p. 183-221 39 p.Research output: Contribution to journal › Article › Research › peer-review
10 Citations (Scopus) -
L2-BOUNDEDNESS OF GRADIENTS OF SINGLE-LAYER POTENTIALS AND UNIFORM RECTIFIABILITY
Prat, L., Puliatti, C. & Tolsa, X., 2021, In: Analysis and PDE. 14, 3, p. 717-791 75 p.Research output: Contribution to journal › Article › Research › peer-review
4 Citations (Scopus) -
Removable singularities for Lipschitz caloric functions in time varying domains
Mateu, J., Prat, L. & Tolsa, X., 21 Jun 2021, In: Revista Matematica Iberoamericana. 38, 2, p. 547-588 42 p.Research output: Contribution to journal › Article › Research › peer-review
Open Access3 Citations (Scopus) -
The Mutual Singularity of Harmonic Measure and Hausdorff Measure of Codimension Smaller than One
Tolsa, X., 1 Sept 2021, In: International Mathematics Research Notices. 2021, 18, p. 13783-13811 29 p.Research output: Contribution to journal › Article › Research › peer-review
Open Access1 Citation (Scopus) -
Unique Continuation at the Boundary for Harmonic Functions in C1 Domains and Lipschitz Domains with Small Constant
Tolsa, X., 1 Jan 2021, In: Communications on Pure and Applied Mathematics.Research output: Contribution to journal › Article › Research › peer-review
Open Access6 Citations (Scopus) -
2020
A family of singular integral operators which control the Cauchy transform
Chunaev, P., Mateu, J. & Tolsa, X., 1 Apr 2020, In: Mathematische Zeitschrift. 294, 3-4, p. 1283-1340 58 p.Research output: Contribution to journal › Article › Research › peer-review
3 Citations (Scopus) -
Analytic capacity and projections
Chang, A. & Tolsa, X., 5 Oct 2020, In: Journal of the European Mathematical Society. 22, 12, p. 4121-4159 39 p.Research output: Contribution to journal › Article › Research › peer-review
3 Citations (Scopus) -
A two-phase free boundary problem for harmonic measure and uniform rectifiability
Azzam, J., Mourgoglou, M. & Tolsa, X., 1 Jun 2020, In: Transactions of the American Mathematical Society. 373, 6, p. 4359-4388 30 p.Research output: Contribution to journal › Article › Research › peer-review
4 Citations (Scopus) -
Characterization of rectifiable measures in terms of α-numbers
AZZAM, J., TOLSA, X. & TORO, T., 1 Jan 2020, In: Transactions of the American Mathematical Society. 373, 11, p. 7991-8037 47 p.Research output: Contribution to journal › Article › Research › peer-review
5 Citations (Scopus) -
Harmonic measure and quantitative connectivity: geometric characterization of the Lp -solvability of the Dirichlet problem
Azzam, J., Hofmann, S., Martell, J. M., Mourgoglou, M. & Tolsa, X., 1 Dec 2020, In: Inventiones Mathematicae. 222, 3, p. 881-993 113 p.Research output: Contribution to journal › Article › Research › peer-review
35 Citations (Scopus) -
Jump formulas for singular integrals and layer potentials on rectifiable sets
Tolsa, X., 1 Nov 2020, In: Proceedings of the American Mathematical Society. 148, 11, p. 4755-4767 13 p.Research output: Contribution to journal › Article › Research › peer-review
7 Citations (Scopus) -
The Riesz Transform of Codimension Smaller Than One and the Wolff Energy
Jaye, B., Nazarov, F., Reguera, M. C. & Tolsa, X., 1 Jul 2020, In: Memoirs of the American Mathematical Society. 266, 1293, p. 1-110 110 p.Research output: Contribution to journal › Article › Research › peer-review
1 Citation (Scopus) -
The two-phase problem for harmonic measure in VMO
Prats, M. & Tolsa, X., 1 Jun 2020, In: Calculus of Variations and Partial Differential Equations. 59, 3Research output: Contribution to journal › Article › Research › peer-review
Open Access5 Citations (Scopus)1 Downloads (Pure) -
2019
Failure of L 2 boundedness of gradients of single layer potentials for measures with zero low density
Conde-Alonso, J. M., Mourgoglou, M. & Tolsa, X., 8 Feb 2019, In: Mathematische Annalen. 373, p. 253-285Research output: Contribution to journal › Article › Research
6 Citations (Scopus) -
On a two-phase problem for harmonic measure in general domains
Azzam, J., Mourgoglou, M., Tolsa, X. & Volberg, A., 1 Oct 2019, In: American Journal of Mathematics. 141, p. 1259-1279Research output: Contribution to journal › Article › Research
9 Citations (Scopus) -
On C1 -approximability of functions by solutions of second order elliptic equations on plane compact sets and C-analytic capacity
Paramonov, P. V. & Tolsa, X., 1 Sept 2019, In: Analysis and Mathematical Physics. 9, p. 1133-1161Research output: Contribution to journal › Article › Research
1 Citation (Scopus) -
Rectifiability of measures and the β<inf>p</inf> coefficients
Tolsa, X., 1 Jan 2019, In: Publicacions Matematiques. 63, 2, p. 491-519 29 p.Research output: Contribution to journal › Review article › Research › peer-review
9 Citations (Scopus) -
Singular integrals unsuitable for the curvature method whose L 2-boundedness still implies rectifiability
Chunaev, P., Mateu, J. & Tolsa, X., 1 Oct 2019, In: Journal d'Analyse Mathematique. 138, p. 741-764Research output: Contribution to journal › Article › Research
2 Citations (Scopus) -
2018
Improved Cotlar's inequality in the context of local Tb theorems
Martikainen, H., Mourgoglou, M. & Tolsa, X., 1 Mar 2018, In: Journal of Functional Analysis. 274, 5, p. 1255-1275Research output: Contribution to journal › Article › Research › peer-review
3 Citations (Scopus) -
On Tsirelson’s theorem about triple points for harmonic measure
Tolsa, X. & Volberg, A., 1 Jun 2018, In: International Mathematics Research Notices. 2018, 12, p. 3671-3683Research output: Contribution to journal › Article › Research › peer-review
3 Citations (Scopus) -
The measures with an associated square function operator bounded in L2
Jaye, B., Nazarov, F. & Tolsa, X., 1 Dec 2018, In: Advances in Mathematics. 339, p. 60-112Research output: Contribution to journal › Article › Research
3 Citations (Scopus) -
The Riesz transform and quantitative rectifiability for general Radon measures
Girela-Sarrión, D. & Tolsa, X., 1 Feb 2018, In: Calculus of Variations and Partial Differential Equations. 57, 1, 16.Research output: Contribution to journal › Article › Research › peer-review
7 Citations (Scopus) -
Uniform rectifiability from Carleson measure estimates and ε-approximability of bounded harmonic functions
Garnett, J., Mourgoglou, M. & Tolsa, X., 1 Jan 2018, In: Duke Mathematical Journal. 167, 8, p. 1473-1524Research output: Contribution to journal › Article › Research › peer-review
28 Citations (Scopus) -
2017
Lp estimates for the variation for singular integrals on uniformly rectifiable sets
Mas, A. & Tolsa, X., 1 Jan 2017, In: Transactions of the American Mathematical Society. 369, 11, p. 8239-8275Research output: Contribution to journal › Article › Research › peer-review
6 Citations (Scopus) -
Mutual Absolute Continuity of Interior and Exterior Harmonic Measure Implies Rectifiability
Azzam, J., Mourgoglou, M. & Tolsa, X., 1 Nov 2017, In: Communications on Pure and Applied Mathematics. 70, 11, p. 2121-2163Research output: Contribution to journal › Article › Research › peer-review
19 Citations (Scopus) -
Rectifiable measures, square functions involving densities, and the Cauchy transform
Tolsa, X., 1 Jan 2017, In: Memoirs of the American Mathematical Society. 245, 1158, p. 1-134Research output: Contribution to journal › Article › Research › peer-review
14 Citations (Scopus) -
The one-phase problem for harmonic measure in two-sided NTA domains
Azzam, J., Mourgoglou, M. & Tolsa, X., 1 Jan 2017, In: Analysis and PDE. 10, 3, p. 559-588Research output: Contribution to journal › Article › Research › peer-review
3 Citations (Scopus) -
2016
Harmonic measure is rectifiable if it is absolutely continuous with respect to the co-dimension-one Hausdorff measure
Azzam, J., Hofmann, S., Martell, J. M., Mayboroda, S., Mourgoglou, M., Tolsa, X. & Volberg, A., 1 Apr 2016, In: Comptes Rendus Mathematique. 354, 4, p. 351-355Research output: Contribution to journal › Article › Research › peer-review
3 Citations (Scopus) -
Rectifiability of harmonic measure
Azzam, J., Hofmann, S., Martell, J. M., Mayboroda, S., Mourgoglou, M., Tolsa, X. & Volberg, A., 1 Jun 2016, In: Geometric and Functional Analysis. 26, 3, p. 703-728Research output: Contribution to journal › Article › Research › peer-review
53 Citations (Scopus) -
Riesz transforms of non-integer homogeneity on uniformly disconnected sets
Reguera, M. C. & Tolsa, X., 1 Oct 2016, In: Transactions of the American Mathematical Society. 368, 10, p. 7045-7095Research output: Contribution to journal › Article › Research › peer-review
4 Citations (Scopus) -
Square functions and uniform rectifiability
Chousionis, V., Garnett, J., Le, T. & Tolsa, X., 1 Jan 2016, In: Transactions of the American Mathematical Society. 368, 9, p. 6063-6102Research output: Contribution to journal › Article › Research › peer-review
5 Citations (Scopus) -
Square Functions of Fractional Homogeneity and Wolff Potentials
Chousionis, V., Prat, L. & Tolsa, X., 1 Jan 2016, In: International Mathematics Research Notices. 2016, 8, p. 2295-2319Research output: Contribution to journal › Article › Research › peer-review
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2015
A T(P) theorem for Sobolev spaces on domains
Prats, M. & Tolsa Domènech, X., 1 Jan 2015, In: Journal of Functional Analysis. 268, 10, p. 2946-2989 44 p.Research output: Contribution to journal › Article › Research › peer-review
Open Access18 Citations (Scopus)1 Downloads (Pure) -
Characterization of n-rectifiability in terms of Jones’ square function: part I
Tolsa, X., 1 Dec 2015, In: Calculus of Variations and Partial Differential Equations. 54, 4, p. 3643-3665Research output: Contribution to journal › Article › Research › peer-review
32 Citations (Scopus) -
Characterization of n-rectifiability in terms of Jones’ square function: Part II
Azzam, J. & Tolsa, X., 1 Oct 2015, In: Geometric and Functional Analysis. 25, 5, p. 1371-1412Research output: Contribution to journal › Article › Research › peer-review
52 Citations (Scopus) -
NON-EXISTENCE OF REFLECTIONLESS MEASURES FOR THE s-RIESZ TRANSFORM WHEN 0 < s < 1
Prat, L. & Tolsa, X., 1 Jan 2015, In: Annales Academiae Scientiarum Fennicae Mathematica. 40, p. 957-968 12 p.Research output: Contribution to journal › Article › Research › peer-review
2 Citations (Scopus) -
Rectifiability via a square function and Preiss' theorem
Tolsa, X. & Toro, T., 1 Jan 2015, In: International Mathematics Research Notices. 2015, 13, p. 4638-4662Research output: Contribution to journal › Article › Research › peer-review
13 Citations (Scopus) -
2014
Analytic capacity
Tolsa, X., 1 Jan 2014, Progress in Mathematics. Vol. 307. p. 15-43 28 p.Research output: Chapter in Book › Chapter › Research › peer-review
1 Citation (Scopus) -
A Tb theorem of Nazarov, Treil and Volberg
Tolsa, X., 1 Jan 2014, Progress in Mathematics. Vol. 307. p. 137-194 57 p.Research output: Chapter in Book › Chapter › Research › peer-review
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Basic calderón-zygmund theory with non-doubling measures
Tolsa, X., 1 Jan 2014, Progress in Mathematics. Vol. 307. p. 45-74 29 p.Research output: Chapter in Book › Chapter › Research › peer-review
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Basic notation
Tolsa, X., 1 Jan 2014, Progress in Mathematics. Vol. 307. p. 11-13 2 p.Research output: Chapter in Book › Chapter › Research › peer-review
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Curvature and rectifiability
Tolsa, X., 1 Jan 2014, Progress in Mathematics. Vol. 307. p. 231-288 57 p.Research output: Chapter in Book › Chapter › Research › peer-review
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On the uniform rectifiability of AD-regular measures with bounded Riesz transform operator: the case of codimension 1
Nazarov, F., Volberg, A. & Tolsa, X., 1 Jan 2014, In: Acta Mathematica. 213, 2, p. 237-321Research output: Contribution to journal › Article › Research › peer-review
83 Citations (Scopus) -
Principal values for the Cauchy transform and rectifiability
Tolsa, X., 1 Jan 2014, Progress in Mathematics. Vol. 307. p. 289-317 28 p.Research output: Chapter in Book › Chapter › Research › peer-review
1 Citation (Scopus) -
RBMO(μ) and H<sup>1</sup><inf>atb</inf>(μ)
Tolsa, X., 1 Jan 2014, Progress in Mathematics. Vol. 307. p. 319-379 60 p.Research output: Chapter in Book › Chapter › Research › peer-review
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Strong and weak type estimates for singular integrals with respect to measures separated by AD-regular boundaries
Chousionis, V. & Tolsa, X., 1 Jan 2014, In: International Mathematics Research Notices. 2014, 23, p. 6497-6522Research output: Contribution to journal › Article › Research › peer-review
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The capacity γ+
Tolsa, X., 1 Jan 2014, Progress in Mathematics. Vol. 307. p. 103-135 32 p.Research output: Chapter in Book › Chapter › Research › peer-review
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The cauchy transform and menger curvature
Tolsa, X., 1 Jan 2014, Progress in Mathematics. Vol. 307. p. 75-101 26 p.Research output: Chapter in Book › Chapter › Research › peer-review