Weighted Rellich inequality is obtained in variable exponent Lebesgue spaces. Two-sided estimates of the measure of non-compactness for the two-weighted Hardy operator are derived in \(L^{p(\cdot )}\) spaces. Further, weighted multilinear Rellich and Hardy estimates are obtained in one-dimensional case.

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Rellich Inequality

  • Alexander Meskhi,
  • Humberto Rafeiro,
  • Stefan Samko

摘要

Weighted Rellich inequality is obtained in variable exponent Lebesgue spaces. Two-sided estimates of the measure of non-compactness for the two-weighted Hardy operator are derived in \(L^{p(\cdot )}\) spaces. Further, weighted multilinear Rellich and Hardy estimates are obtained in one-dimensional case.