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<p>We characterize by means of kernel <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\phi \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ϕ</mi> </math></EquationSource> </InlineEquation> and measurable function <i>a</i> such that the generalized Hausdorff operator and its adjoint operator are bounded on the Cesàro second-order function spaces <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(Ces_p^2(\mathbb {R}^{+}),\ 1&lt;p\le \infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>C</mi> <mi>e</mi> <msubsup> <mi>s</mi> <mi>p</mi> <mn>2</mn> </msubsup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mo>+</mo> </msup> <mo stretchy="false">)</mo> </mrow> <mo>,</mo> <mspace width="4pt" /> <mn>1</mn> <mo>&lt;</mo> <mi>p</mi> <mo>≤</mo> <mi>∞</mi> </mrow> </math></EquationSource> </InlineEquation>. We also study the analogous problem for Erdélyi-Kober and Mellin fractional integrals, and determine their adjoint operators on <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(Ces_p^2(\mathbb {R}^{+})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>C</mi> <mi>e</mi> <msubsup> <mi>s</mi> <mi>p</mi> <mn>2</mn> </msubsup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mo>+</mo> </msup> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> under certain conditions on <i>p</i>.</p>

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INTEGRAL OPERATORS ON CESÀRO SECOND-ORDER FUNCTION SPACES

  • 期刊论文

  • 发表日期：

    2026年3月23日

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  • Sangeerthana R,
  • Kalaivani Kamalakkannan

摘要

We characterize by means of kernel \(\phi \) ϕ and measurable function a such that the generalized Hausdorff operator and its adjoint operator are bounded on the Cesàro second-order function spaces \(Ces_p^2(\mathbb {R}^{+}),\ 1<p\le \infty \) C e s p 2 ( R + ) , 1 < p ≤ ∞ . We also study the analogous problem for Erdélyi-Kober and Mellin fractional integrals, and determine their adjoint operators on \(Ces_p^2(\mathbb {R}^{+})\) C e s p 2 ( R + ) under certain conditions on p.