Geodesic
A new approach for Hardy spaces with variable exponents on spaces of homogeneous type
Filomat, Tome 37 (2023) no. 23, p. 7719

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

DOI

In the paper, we establish and study Hardy spaces with variable exponents on spaces of homogeneous type (X, d, µ) in the sense of Coifman and Weiss, where d may have no any regularity property and µ fulfills the doubling property only. First we introduce the Hardy spaces with variable exponents H p(·) (X) by using the wavelet Littlewood–Paley square functions and give their equivalent characterizations. Then we establish the atomic characterization theory for H p(·) (X) via the new Calderón-type reproducing identity and the Littlewood–Paley–Stein theory. Finally, we give a unified method for defining these variable Hardy spaces H p(·) (X) in terms of the same spaces of test functions and distributions. More precisely, we introduce the variable Carleson measure spaces CMO p(·) L 2 (X) and characterize the variable Hardy spaces via the distributions of CMO p(·) L 2 (X).
DOI : 10.2298/FIL2323719T
Classification : 42B30, 42B25, 43A85
Keywords: Hardy space with variable exponents, Carleson measure space, wavelet reproducing identity, Littlewood–Paley–Stein characterization, space of homogeneous type 
Jian Tan. A new approach for Hardy spaces with variable exponents on spaces of homogeneous type. Filomat, Tome 37 (2023) no. 23, p. 7719 . doi: 10.2298/FIL2323719T
@article{10_2298_FIL2323719T,
     author = {Jian Tan},
     title = {A new approach for {Hardy} spaces with variable exponents on spaces of homogeneous type},
     journal = {Filomat},
     pages = {7719 },
     year = {2023},
     volume = {37},
     number = {23},
     doi = {10.2298/FIL2323719T},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2323719T/}
}
TY  - JOUR
AU  - Jian Tan
TI  - A new approach for Hardy spaces with variable exponents on spaces of homogeneous type
JO  - Filomat
PY  - 2023
SP  - 7719 
VL  - 37
IS  - 23
UR  - http://geodesic.mathdoc.fr/articles/10.2298/FIL2323719T/
DO  - 10.2298/FIL2323719T
LA  - en
ID  - 10_2298_FIL2323719T
ER  - 
%0 Journal Article
%A Jian Tan
%T A new approach for Hardy spaces with variable exponents on spaces of homogeneous type
%J Filomat
%D 2023
%P 7719 
%V 37
%N 23
%U http://geodesic.mathdoc.fr/articles/10.2298/FIL2323719T/
%R 10.2298/FIL2323719T
%G en
%F 10_2298_FIL2323719T

Cité par Sources :