Convergence of singular integrals with general measures

Pertti Mattila; Joan Verdera

doi:10.4171/JEMS/149

Convergence of singular integrals with general measures

Pertti Mattila, Joan Verdera

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Resum

We show that L2-bounded singular integrals in metric spaces with respect to general measures and kernels converge weakly. This implies a kind of average convergence almost everywhere. For measures with zero density we prove the almost everywhere existence of principal values. © European Mathematical Society 2009.

Idioma original	Anglès
Pàgines (de-a)	257-271
Revista	Journal of the European Mathematical Society
Volum	11
Número	2
DOIs	https://doi.org/10.4171/JEMS/149
Estat de la publicació	Publicada - 1 de gen. 2009

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@article{798e06632183475f957a928c7f1ebaea,

title = "Convergence of singular integrals with general measures",

abstract = "We show that L2-bounded singular integrals in metric spaces with respect to general measures and kernels converge weakly. This implies a kind of average convergence almost everywhere. For measures with zero density we prove the almost everywhere existence of principal values. {\textcopyright} European Mathematical Society 2009.",

keywords = "Singular integrals, Martingales, Principal values",

author = "Pertti Mattila and Joan Verdera",

year = "2009",

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doi = "10.4171/JEMS/149",

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AU - Verdera, Joan

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AB - We show that L2-bounded singular integrals in metric spaces with respect to general measures and kernels converge weakly. This implies a kind of average convergence almost everywhere. For measures with zero density we prove the almost everywhere existence of principal values. © European Mathematical Society 2009.

KW - Singular integrals

KW - Martingales

KW - Principal values

UR - https://dialnet.unirioja.es/servlet/articulo?codigo=2976038

UR - https://www.scopus.com/pages/publications/74249093364

U2 - 10.4171/JEMS/149

DO - 10.4171/JEMS/149

M3 - Article

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SP - 257

EP - 271

JO - Journal of the European Mathematical Society

JF - Journal of the European Mathematical Society

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ER -

Convergence of singular integrals with general measures

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