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Volume 38, Issue 4
Some Estimates for $θ$-Type Calderόn–Zygmund Operators and Linear Commutators on Certain Weighted Amalgam Spaces

Hua Wang

DOI: 10.4208/ata.OA-2020-0034

Anal. Theory Appl., 38 (2022), pp. 361-393.

Published online: 2023-01

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  • Abstract

In this paper, we first introduce some new kinds of weighted amalgam spaces. Then we discuss the strong type and weak type estimates for a class of Calderόn–Zygmund type operators $T_θ$ in these new weighted spaces. Furthermore, the strong type estimate and endpoint estimate of linear commutators $[b, T_θ]$ formed by $b$ and $T_θ$ are established. Also we study related problems about two-weight, weak type inequalities for $T_θ$ and $[b, T_θ]$ in the weighted amalgam spaces and give some results.

  • Keywords

$θ$-type Calderόn–Zygmund operators, commutators, weighted amalgam spaces, Muckenhoupt weights, Orlicz spaces.

  • AMS Subject Headings

42B20, 42B35, 46E30, 47B47

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{ATA-38-361, author = {Wang , Hua}, title = {Some Estimates for $θ$-Type Calderόn–Zygmund Operators and Linear Commutators on Certain Weighted Amalgam Spaces}, journal = {Analysis in Theory and Applications}, year = {2023}, volume = {38}, number = {4}, pages = {361--393}, abstract = {

In this paper, we first introduce some new kinds of weighted amalgam spaces. Then we discuss the strong type and weak type estimates for a class of Calderόn–Zygmund type operators $T_θ$ in these new weighted spaces. Furthermore, the strong type estimate and endpoint estimate of linear commutators $[b, T_θ]$ formed by $b$ and $T_θ$ are established. Also we study related problems about two-weight, weak type inequalities for $T_θ$ and $[b, T_θ]$ in the weighted amalgam spaces and give some results.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2020-0034}, url = {http://global-sci.org/intro/article_detail/ata/21355.html} }
TY - JOUR T1 - Some Estimates for $θ$-Type Calderόn–Zygmund Operators and Linear Commutators on Certain Weighted Amalgam Spaces AU - Wang , Hua JO - Analysis in Theory and Applications VL - 4 SP - 361 EP - 393 PY - 2023 DA - 2023/01 SN - 38 DO - http://doi.org/10.4208/ata.OA-2020-0034 UR - https://global-sci.org/intro/article_detail/ata/21355.html KW - $θ$-type Calderόn–Zygmund operators, commutators, weighted amalgam spaces, Muckenhoupt weights, Orlicz spaces. AB -

In this paper, we first introduce some new kinds of weighted amalgam spaces. Then we discuss the strong type and weak type estimates for a class of Calderόn–Zygmund type operators $T_θ$ in these new weighted spaces. Furthermore, the strong type estimate and endpoint estimate of linear commutators $[b, T_θ]$ formed by $b$ and $T_θ$ are established. Also we study related problems about two-weight, weak type inequalities for $T_θ$ and $[b, T_θ]$ in the weighted amalgam spaces and give some results.

Hua Wang. (2023). Some Estimates for $θ$-Type Calderόn–Zygmund Operators and Linear Commutators on Certain Weighted Amalgam Spaces. Analysis in Theory and Applications. 38 (4). 361-393. doi:10.4208/ata.OA-2020-0034
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