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<p>In this paper we consider a class of sublinear operators which include the fractional integrals related to the operators with Gaussian kernel bounds, fractional integral operators with rough kernels, and fractional maximal operators with rough kernels, and include the maximal operators, Calderón–Zygmund operators, Carleson type maximal operators, C. Fefferman’s singular multipliers, and many others as special cases. We investigate the boundedness of the sublinear operators in various types of generalization of Morrey spaces, namely generalized weighted Morrey spaces, vanishing generalized weighted Morrey spaces, generalized weighted mixed-Morrey spaces, generalized weighted local-Morrey spaces, vanishing generalized weighted local-Morrey spaces, and generalized weighted global-Morrey spaces with variable exponent. Under some assumptions, we prove that the operators and their higher order commutator with a BMO function are bounded on those function spaces with different weights.</p>

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Two-Weighted Estimates for Some Sublinear Operators and Their Higher Order Commutators in Various Types of Generalizations of Morrey Spaces with Variable Exponent

  • 期刊论文

  • 发表日期：

    2025年8月12日

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  • Yusuf Ramadana

摘要

In this paper we consider a class of sublinear operators which include the fractional integrals related to the operators with Gaussian kernel bounds, fractional integral operators with rough kernels, and fractional maximal operators with rough kernels, and include the maximal operators, Calderón–Zygmund operators, Carleson type maximal operators, C. Fefferman’s singular multipliers, and many others as special cases. We investigate the boundedness of the sublinear operators in various types of generalization of Morrey spaces, namely generalized weighted Morrey spaces, vanishing generalized weighted Morrey spaces, generalized weighted mixed-Morrey spaces, generalized weighted local-Morrey spaces, vanishing generalized weighted local-Morrey spaces, and generalized weighted global-Morrey spaces with variable exponent. Under some assumptions, we prove that the operators and their higher order commutator with a BMO function are bounded on those function spaces with different weights.