Fractional maximal operator in the local Morrey–Lorentz spaces and some applications

IF 0.9 Q2 MATHEMATICS
V. S. Guliyev, C. Aykol, A. Kucukaslan, A. Serbetci
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引用次数: 0

Abstract

In this study, we obtain the necessary and sufficient conditions for the boundedness of the fractional maximal operator \(M_{\alpha }\) in the local Morrey–Lorentz spaces \(M_{p,q;\lambda }^{loc}({\mathbb {R}}^n)\). We use sharp rearrangement inequalities while proving our result. We apply this result to the Schrödinger operator \(-\Delta + V\) on \({\mathbb {R}}^n\), where the nonnegative potential V belongs to the reverse Hölder class \(B_{\infty }({\mathbb {R}}^n)\). The local Morrey–Lorentz \(M_{p,r;\lambda }^{loc}({\mathbb {R}}^n) \rightarrow M_{q,s;\lambda }^{loc}({\mathbb {R}}^n)\) estimates for the Schrödinger type operators \(V^{\gamma } (-\Delta +V)^{-\beta }\) and \(V^{\gamma } \nabla (-\Delta +V)^{-\beta }\) are obtained.

局部Morrey-Lorentz空间中的分数极大算子及其应用
在本研究中,我们得到了局部Morrey-Lorentz空间\(M_{p,q;\lambda }^{loc}({\mathbb {R}}^n)\)上分数极大算子\(M_{\alpha }\)有界的充分必要条件。在证明结果时,我们使用了尖锐重排不等式。我们将此结果应用于\({\mathbb {R}}^n\)上的Schrödinger算子\(-\Delta + V\),其中非负势V属于反向Hölder类\(B_{\infty }({\mathbb {R}}^n)\)。得到了Schrödinger型算子\(V^{\gamma } (-\Delta +V)^{-\beta }\)和\(V^{\gamma } \nabla (-\Delta +V)^{-\beta }\)的局部Morrey-Lorentz \(M_{p,r;\lambda }^{loc}({\mathbb {R}}^n) \rightarrow M_{q,s;\lambda }^{loc}({\mathbb {R}}^n)\)估计。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Afrika Matematika
Afrika Matematika MATHEMATICS-
CiteScore
2.00
自引率
9.10%
发文量
96
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