Abstract
We reduce the boundedness of operators in Morrey spaces \(L_p^r\left( {\mathbb R}^n\right) \), its preduals, \(H^{\varrho }L_p ({\mathbb R}^n)\), and their preduals \(\overset{\circ }{L}{}^r_{p}\left( \mathbb {R}^n\right) \) to the boundedness of the appropriate operators in Lebesgue spaces, \(L_p({\mathbb R}^n)\). Hereby, we need a weak condition with respect to the operators which is satisfied for a large set of classical operators of harmonic analysis including singular integral operators and the Hardy-Littlewood maximal function. The given vector-valued consideration of these issues is a key ingredient for various applications in harmonic analysis.
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Communicated by Loukas Grafakos.
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Rosenthal, M., Schmeisser, HJ. On the Boundedness of Singular Integrals in Morrey Spaces and its Preduals. J Fourier Anal Appl 22, 462–490 (2016). https://doi.org/10.1007/s00041-015-9427-9
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DOI: https://doi.org/10.1007/s00041-015-9427-9