Boundedness of the Maximal, Potential and Singular Operators in the Generalized Morrey Spaces

By Vagif S. Guliyev. 2009

208 citations recorded by the source corpus.

We consider generalized Morrey spaces with a general function defining the Morrey-type norm. We find the conditions on the pair which ensures the boundedness of the maximal operator and Calderón-Zygmund singular integral operators from one generalized Morrey space to another , , and from the space to the weak space . We also prove a Sobolev-Adams type -theorem for the potential operators . In all the cases the conditions for the boundedness are given it termsof Zygmund-type integral inequalities on , which do not assume any assumption on monotonicity of in . As applications, we establish the boundedness of some Schrödinger type operators on generalized Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class. As an another application, we prove the boundedness of various operators on generalized Morrey spaces which are estimated by Riesz potentials.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/1ad9ddcdda9924afaaf5f5e862c2417fcc7e86a3

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In Applied Mathematics

1. Yoshihiro Sawano
2. S. Samko
3. Vagif S. Guliyev
4. F. Deringoz
5. Kwok-Pun Ho
6. E. Nakai
7. Dachun Yang
8. Wen Yuan

In Mathematical Physics

1. Yoshihiro Sawano
2. S. Samko
3. Vagif S. Guliyev
4. F. Deringoz
5. Dachun Yang
6. Kwok-Pun Ho
7. Wen Yuan
8. E. Nakai

Citations in the corpus

• Boundedness of the Maximal and Singular Operators on Generalized Orlicz–Morrey Spaces (2013, background): “The following statement, containing results obtained in [13, 14, 15, 27, 30] was proved in [1] (see also [16]).”
• A Thought on Generalized Morrey Spaces (2018, background): “See [4, 30, 46, 76] for the approach to this direction.”
• Generalized Local Morrey Spaces and Fractional Integral Operators with Rough Kernel (2012, background): “The following statements, containing results obtained in [34], [36] was proved in [26, 28] (see also [5]-[8], [27, 29]). where C does not depend on r .”
• On the boundedness of the maximal operator and singular integral operators in generalized Morrey spaces (2012, unknown): “The following statement, containing the results in [14], [17] was proved in [10] (see also [11], [12]).”