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Hausdorff operator on Morrey spaces and Campanato spaces

Jianmiao Ruan, Dashan Fan, Hongliang Li (2020)

Czechoslovak Mathematical Journal

We study the high-dimensional Hausdorff operators on the Morrey space and on the Campanato space. We establish their sharp boundedness on these spaces. Particularly, our results solve an open question posted by E. Liflyand (2013).

Homeomorphisms acting on Besov and Triebel-Lizorkin spaces of local regularity ψ(t).

Silvia I. Hartzstein, Beatriz E. Viviani (2005)

Collectanea Mathematica

The aim of this paper is to show that the integral and derivative operators defined by local regularities are homeomorphisms for generalized Besov and Triebel-Lizorkin spaces with local regularities. The underlying geometry is that of homogeneous type spaces and the functions defining local regularities belong to a larger class of growth functions than the potentials tα, related to classical fractional integral and derivative operators and Besov and Triebel-Lizorkin spaces.

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