Dilation operators and integral operators on amalgam space \((L_{p},l_{q})\)

Abstract

This paper establishes the Hardy–Littlewood–Pólya inequalities, the Hardy inequalities and the Hilbert inequalities on amalgam spaces. Moreover, it also gives the mapping properties of the Mellin convolutions, the Hadamard fractional integrals and the Hausdorff operators on amalgam spaces. We establish these properties by some estimates for the operator norms of the dilation operators on amalgam spaces.

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Correspondence to Kwok-Pun Ho.

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Ho, K. Dilation operators and integral operators on amalgam space \((L_{p},l_{q})\). Ricerche mat 68, 661–677 (2019). https://doi.org/10.1007/s11587-019-00431-5

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Keywords

  • Amalgam spaces
  • Integral operator
  • Hardy inequality
  • Hilbert inequality
  • Hadamard fractional integral
  • Mellin convolution
  • Hausdorff operator

Mathematics Subject Classification

  • 26D10
  • 26D15
  • 42B35
  • 44A05
  • 46E30