Weighted estimates of commutators of singular operators in generalized Morrey spaces beyond Muckenhoupt range and applications
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https://hdl.handle.net/10037/34891Date
2024-05-30Type
Journal articleTidsskriftartikkel
Peer reviewed
Author
Samko, Natasha GabatsuyevnaAbstract
For a certain class of radial weights, we prove weighted norm estimates for commutators with BMO coefficients of singular operators in local generalized Morrey spaces.
As a consequence of these estimates, we obtain norm inequalities for such commutators in the generalized Stummel-Morrey spaces. We also discuss a.e. well-posedness of
singular operators and their commutators on weighted generalized Morrey spaces. The
obtained estimates are applied to prove interior regularity for solutions of elliptic PDEs
in the frameworks of the corresponding weighted Sobolev spaces based on the local
generalized Morrey spaces or Stummel-Morrey spaces. To this end also conditions
for the applicability of the representation formula, for the second-order derivatives
of solutions to elliptic PDEs, are found for the case of such weighted spaces. In both
results, for commutators and applications, we admit weights beyond the Muckenhoupt
range.
Publisher
Springer NatureCitation
Samko. Weighted estimates of commutators of singular operators in generalized Morrey spaces beyond Muckenhoupt range and applications. Analysis and Mathematical Physics. 2024;14(3)Metadata
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