Non-collapsing condition and Sobolev embeddings for Hajłasz-Besov spaces

Joaquím Martín; Walter A. Ortiz

doi:10.1007/s11117-025-01115-1

Non-collapsing condition and Sobolev embeddings for Hajłasz-Besov spaces

Joaquím Martín, Walter A. Ortiz

Universidad Internacional de Valencia (VIU)

Producció científica: Contribució a revista › Article › Recerca › Avaluat per experts

1 Citació (Scopus)

Resum

In this paper we will focus on understanding the relationship between Sobolev embedding theorems for Hajłasz-Besov spaces defined on a doubling metric measure space (Ω,d,μ) and the non-collapsing condition of the measure, i.e. (Formula presented.) We will also obtain embedding results for Hajłasz-Besov spaces whose modulus of smoothness is generated by a rearrangement invariant quasi-norm.

Idioma original	Anglès
Número d’article	23
Nombre de pàgines	43
Revista	Positivity
Volum	29
DOIs	https://doi.org/10.1007/s11117-025-01115-1
Estat de la publicació	Publicada - 12 de març 2025

Accés al document

10.1007/s11117-025-01115-1

https://ddd.uab.cat/record/310502

Altres arxius i enllaços

Com citar-ho

@article{28ead7e7c274469d8159f2d15825a7b4,

title = "Non-collapsing condition and Sobolev embeddings for Haj{\l}asz-Besov spaces",

abstract = "In this paper we will focus on understanding the relationship between Sobolev embedding theorems for Haj{\l}asz-Besov spaces defined on a doubling metric measure space (Ω,d,μ) and the non-collapsing condition of the measure, i.e. (Formula presented.) We will also obtain embedding results for Haj{\l}asz-Besov spaces whose modulus of smoothness is generated by a rearrangement invariant quasi-norm.",

keywords = "Fractional Haj{\l}asz–Sobolev spaces, Haj{\l}asz–Besov spaces, Interpolation, Metric measure spaces, Rearrangement invariant spaces, Sobolev inequality",

author = "Joaqu{\'i}m Mart{\'i}n and Ortiz, \{Walter A.\}",

note = "Publisher Copyright: {\textcopyright} The Author(s) 2025.",

year = "2025",

month = mar,

day = "12",

doi = "10.1007/s11117-025-01115-1",

language = "English",

volume = "29",

journal = "Positivity",

issn = "1385-1292",

publisher = "Birkhauser Verlag Basel",

}

TY - JOUR

T1 - Non-collapsing condition and Sobolev embeddings for Hajłasz-Besov spaces

AU - Martín, Joaquím

AU - Ortiz, Walter A.

N1 - Publisher Copyright: © The Author(s) 2025.

PY - 2025/3/12

Y1 - 2025/3/12

N2 - In this paper we will focus on understanding the relationship between Sobolev embedding theorems for Hajłasz-Besov spaces defined on a doubling metric measure space (Ω,d,μ) and the non-collapsing condition of the measure, i.e. (Formula presented.) We will also obtain embedding results for Hajłasz-Besov spaces whose modulus of smoothness is generated by a rearrangement invariant quasi-norm.

AB - In this paper we will focus on understanding the relationship between Sobolev embedding theorems for Hajłasz-Besov spaces defined on a doubling metric measure space (Ω,d,μ) and the non-collapsing condition of the measure, i.e. (Formula presented.) We will also obtain embedding results for Hajłasz-Besov spaces whose modulus of smoothness is generated by a rearrangement invariant quasi-norm.

KW - Fractional Hajłasz–Sobolev spaces

KW - Hajłasz–Besov spaces

KW - Interpolation

KW - Metric measure spaces

KW - Rearrangement invariant spaces

KW - Sobolev inequality

UR - https://www.scopus.com/pages/publications/105000022782

UR - https://www.mendeley.com/catalogue/b38e3c34-2fda-36e8-ae15-c6aa23f18c35/

U2 - 10.1007/s11117-025-01115-1

DO - 10.1007/s11117-025-01115-1

M3 - Article

SN - 1385-1292

VL - 29

JO - Positivity

JF - Positivity

M1 - 23

ER -

Non-collapsing condition and Sobolev embeddings for Hajłasz-Besov spaces

Resum

Accés al document

Altres arxius i enllaços

Fingerprint

Com citar-ho