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Two-weight norm inequalities for rough fractional integral operators on Morrey spaces

Ho Kwok-Pun

Opuscula Mathematica

2024

Vol. 44, no. 1

67--77

We establish the two-weight norm inequalities for the rough fractional integral operators on Morrey spaces.

Zygmund inequality of the conjugate function on Morrey-Zygmund spaces

Yee Tat-Leung, Ho Kwok-Pun

Demonstratio Mathematica

2019

Vol. 52, nr 1

97--104

We generalize the Zygmund inequality for the conjugate function to the Morrey type spaces defined on the unit circle T. We obtain this extended Zygmund inequality by introducing the Morrey-Zygmund space on T.

Characterizations of some function spaces in terms of Haar wavelets

Triebel H.

Commentationes Mathematicae

2013

Vol. 53, No. 2

35--53

Some spaces Asp,q(Rn) with A = {B, F}, s ϵ R, 0 < p, q ≤ ∞, covering Besov spaces, Hölder-Zygmund spaces and Sobolev spaces, admit characterizations in terms of Haar bases. It is the main aim of this paper to extend this observation to corresponding Morreyfied spaces Lr Asp,q(Rn). As a by-product we obtain Littlewood-Paley theorems for (homogeneous and inhomogeneous) Morrey spaces Lrp(Rn), Lrp(Rn) and, in particular, L°rp(Rn).