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<p>We consider multidimensional integral operators with coordinate-wise homogeneous kernels of vector degree <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((-\textbf{1})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mo>-</mo> <mn mathvariant="bold">1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> in anisotropic Morrey spaces. For such operators, we obtain sufficient conditions for boundedness in global and local anisotropic Morrey spaces. If the kernel of the integral operator is non-negative, then we establish the necessary conditions for boundedness. Moreover, for these operators, we find sufficient conditions for boundedness from Lebesgue space to anisotropic Morrey space.</p>

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INTEGRAL OPERATORS WITH COORDINATE-WISE HOMOGENEOUS KERNELS IN ANISOTROPIC MORREY SPACES

  • 期刊论文

  • 发表日期：

    2026年6月27日

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  • Oleg G. Avsyankin

摘要

We consider multidimensional integral operators with coordinate-wise homogeneous kernels of vector degree \((-\textbf{1})\) ( - 1 ) in anisotropic Morrey spaces. For such operators, we obtain sufficient conditions for boundedness in global and local anisotropic Morrey spaces. If the kernel of the integral operator is non-negative, then we establish the necessary conditions for boundedness. Moreover, for these operators, we find sufficient conditions for boundedness from Lebesgue space to anisotropic Morrey space.