This article discusses several definitions of the fractional Laplace operator L=—(—Δ) α/2 in
R d, also known as the Riesz fractional derivative operator; here α∈(0, 2) and d≥ 1. This is …

Title: Morrey spaces: introduction and applications to integral operators and PDE's/Yoshihiro
Sawano, Giuseppe Di Fazio, Denny Ivanal Hakim. Description: First edition.| Boca Raton …

In the present investigation, our aim is to define a generalized subclass of analytic and
biunivalent functions associated with a certain q-integral operator in the open unit disk U …

The main content of this book is composed from two doctoral theses: by VV Katrakhov
(1989) and by SM Sitnik (2016). In our work, for the first time in the format of a monograph …

The real-variable theory of function spaces has always been at the core of harmonic
analysis. In particular, the real-variable theory of the Hardy space is a fundamental tool of …

This survey is aimed at the audience of readers interested in the information on map**
properties of various forms of fractional integration operators, including multidimensional …

This paper is essentially a survey on grand and small Lebesgue spaces, which are
rearrangement-invariant Banach function spaces of interest not only from the point of view of …

This work deals with the m th order elliptic equation with non-smooth coefficients in grand-
Sobolev space generated by the norm of the grand-Lebesgue space L q)(Ω), 1< q<+∞ …

The higher order commutators of fractional integral operator I ζ (⋅), V m of variable order is
shown to be bounded from the grand variable Herz spaces K ̇ p (⋅) a (⋅), u, θ (R n) into the …

Functional Analysis — Weighted extrapolation in grand Morrey spaces and applications to
partial di§erential equations, by Vak Page 1 Rend. Lincei Mat. Appl. 30 (2019), 67–92 DOI …