On the boundedness of singular integrals in Morrey spaces and its preduals

2014/09/02 by Marcel Rosenthal, Rosenthal, Marcel, Hans‐Jürgen Schmeißer +1
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1409.0679

Abstract

We reduce the boundedness of operators in Morrey spaces L_p^r(\mathbb Rⁿ), its preduals, H^\varrhoL_p (\mathbb Rⁿ), and their preduals \overset∘L^r_p(\mathbb Rⁿ) to the boundedness of the appropriate operators in Lebesgue spaces, L_p(\mathbb Rⁿ). 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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