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Boundedness of Bessel–Riesz Operator in Variable Lebesgue Measure Spaces

Author

Listed:
  • Muhammad Nasir

    (Abdus Salam School of Mathematical Sciences, Government College University, 68-B, New Muslim Town, Lahore 54600, Pakistan)

  • Ali Raza

    (Abdus Salam School of Mathematical Sciences, Government College University, 68-B, New Muslim Town, Lahore 54600, Pakistan)

  • Luminiţa-Ioana Cotîrlă

    (Department of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, Romania)

  • Daniel Breaz

    (Department of Mathematics, “1 Decembrie 1918” University of Alba Iulia, 510009 Alba Iulia, Romania)

Abstract

In this manuscript, we establish the boundedness of the Bessel–Riesz operator I α , γ f in variable Lebesgue spaces L p ( · ) . We prove that I α , γ f is bounded from L p ( · ) to L p ( · ) and from L p ( · ) to L q ( · ) . We explore various scenarios for the boundedness of I α , γ f under general conditions, including constraints on the Hardy–Littlewood maximal operator M . To prove these results, we employ the boundedness of M , along with Hölder’s inequality and classical dyadic decomposition techniques. Our findings unify and generalize previous results in classical Lebesgue spaces. In some cases, the results are new even for constant exponents in Lebesgue spaces.

Suggested Citation

  • Muhammad Nasir & Ali Raza & Luminiţa-Ioana Cotîrlă & Daniel Breaz, 2025. "Boundedness of Bessel–Riesz Operator in Variable Lebesgue Measure Spaces," Mathematics, MDPI, vol. 13(3), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:3:p:410-:d:1577563
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