Volume 33, Issue 2
Norm Inequalities for Fractional Integral Operators on Generalized Weighted Morrey Spaces

Anal. Theory Appl., 33 (2017), pp. 93-109.

Published online: 2017-05

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• Abstract

Considering a class of operators which include fractional integrals related to operators with Gaussian kernel bounds, the fractional integral operators with rough kernels and fractional maximal operators with rough kernels as special cases, we prove that if these operators are bounded on weighted Lebesgue spaces and satisfy some local pointwise control, then these operators and the commutators of these operators with a BMO functions are also bounded on generalized weighted Morrey spaces.

42B20, 47G10, 42B35

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@Article{ATA-33-93, author = {}, title = {Norm Inequalities for Fractional Integral Operators on Generalized Weighted Morrey Spaces}, journal = {Analysis in Theory and Applications}, year = {2017}, volume = {33}, number = {2}, pages = {93--109}, abstract = {

Considering a class of operators which include fractional integrals related to operators with Gaussian kernel bounds, the fractional integral operators with rough kernels and fractional maximal operators with rough kernels as special cases, we prove that if these operators are bounded on weighted Lebesgue spaces and satisfy some local pointwise control, then these operators and the commutators of these operators with a BMO functions are also bounded on generalized weighted Morrey spaces.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2017.v33.n2.1}, url = {http://global-sci.org/intro/article_detail/ata/10038.html} }
TY - JOUR T1 - Norm Inequalities for Fractional Integral Operators on Generalized Weighted Morrey Spaces JO - Analysis in Theory and Applications VL - 2 SP - 93 EP - 109 PY - 2017 DA - 2017/05 SN - 33 DO - http://doi.org/10.4208/ata.2017.v33.n2.1 UR - https://global-sci.org/intro/article_detail/ata/10038.html KW - Fractional integral, rough kernel, Gaussian kernel bound, commutator, generalized weighted Morrey space. AB -

Considering a class of operators which include fractional integrals related to operators with Gaussian kernel bounds, the fractional integral operators with rough kernels and fractional maximal operators with rough kernels as special cases, we prove that if these operators are bounded on weighted Lebesgue spaces and satisfy some local pointwise control, then these operators and the commutators of these operators with a BMO functions are also bounded on generalized weighted Morrey spaces.

Y. S. Wang. (1970). Norm Inequalities for Fractional Integral Operators on Generalized Weighted Morrey Spaces. Analysis in Theory and Applications. 33 (2). 93-109. doi:10.4208/ata.2017.v33.n2.1
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