Volume 38, Issue 2
Weighted Norm Inequalities for Marcinkiewicz Integrals with Non-Smooth Kernels on Spaces of Homogeneous Type

Anal. Theory Appl., 38 (2022), pp. 204-231.

Published online: 2022-07

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• Abstract

In this article, we obtain some weighted estimates for Marcinkiewicz integrals with non-smooth kernels on spaces of homogeneous type. The weight $\omega$ considered here belongs to the Muckenhoupt’s class $A_∞.$ Moreover, weighted estimates for commutators of BMO functions and Marcinkiewicz integrals are also given.

• Keywords

Commutators, Muckenhoupt weights, Marcinkiewicz integrals, Singular integrals, Sharp maximal functions, BMO functions, Young functions, Luxemburg norm, Spaces of homogeneous type.

42B20, 42B25, 42B35

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@Article{ATA-38-204, author = {Hung Viet and Le and and 24078 and and Hung Viet Le}, title = {Weighted Norm Inequalities for Marcinkiewicz Integrals with Non-Smooth Kernels on Spaces of Homogeneous Type}, journal = {Analysis in Theory and Applications}, year = {2022}, volume = {38}, number = {2}, pages = {204--231}, abstract = {

In this article, we obtain some weighted estimates for Marcinkiewicz integrals with non-smooth kernels on spaces of homogeneous type. The weight $\omega$ considered here belongs to the Muckenhoupt’s class $A_∞.$ Moreover, weighted estimates for commutators of BMO functions and Marcinkiewicz integrals are also given.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-2019-0011}, url = {http://global-sci.org/intro/article_detail/ata/20799.html} }
TY - JOUR T1 - Weighted Norm Inequalities for Marcinkiewicz Integrals with Non-Smooth Kernels on Spaces of Homogeneous Type AU - Le , Hung Viet JO - Analysis in Theory and Applications VL - 2 SP - 204 EP - 231 PY - 2022 DA - 2022/07 SN - 38 DO - http://doi.org/10.4208/ata.OA-2019-0011 UR - https://global-sci.org/intro/article_detail/ata/20799.html KW - Commutators, Muckenhoupt weights, Marcinkiewicz integrals, Singular integrals, Sharp maximal functions, BMO functions, Young functions, Luxemburg norm, Spaces of homogeneous type. AB -

In this article, we obtain some weighted estimates for Marcinkiewicz integrals with non-smooth kernels on spaces of homogeneous type. The weight $\omega$ considered here belongs to the Muckenhoupt’s class $A_∞.$ Moreover, weighted estimates for commutators of BMO functions and Marcinkiewicz integrals are also given.

Hung Viet Le. (2022). Weighted Norm Inequalities for Marcinkiewicz Integrals with Non-Smooth Kernels on Spaces of Homogeneous Type. Analysis in Theory and Applications. 38 (2). 204-231. doi:10.4208/ata.OA-2019-0011
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