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Weighted Boundedness of Certain Sublinear Operators in Generalized Morrey Spaces on Quasi-Metric Measure Spaces Under the Growth Condition

Permanent link
https://hdl.handle.net/10037/25949
DOI
https://doi.org/10.1007/s00041-022-09924-8
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Date
2022-03-17
Type
Journal article
Tidsskriftartikkel
Peer reviewed

Author
Samko, Natasha Gabatsuyevna
Abstract
We prove weighted boundedness of Calderón–Zygmund and maximal singular operators in generalized Morrey spaces on quasi-metric measure spaces, in general non-homogeneous, only under the growth condition on the measure, for a certain class of weights. Weights and characteristic of the spaces are independent of each other. Weighted boundedness of the maximal operator is also proved in the case when lower and upper Ahlfors exponents coincide with each other. Our approach is based on two important steps. The first is a certain transference theorem, where without use homogeneity of the space, we provide a condition which insures that every sublinear operator with the size condition, bounded in Lebesgue space, is also bounded in generalized Morrey space. The second is a reduction theorem which reduces weighted boundedness of the considered sublinear operators to that of weighted Hardy operators and non-weighted boundedness of some special operators.
Publisher
Springer
Citation
Samko. Weighted Boundedness of Certain Sublinear Operators in Generalized Morrey Spaces on Quasi-Metric Measure Spaces Under the Growth Condition. Journal of Fourier Analysis and Applications. 2022;28
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