The purpose of this note is twofold. First it is a corrigenda of our paper [RV1]. And secondly we make some remarks concerning the interpolation properties of Morrey spaces. 1. Corrigenda. In our paper “Unique continuation for Schrödinger operators with potential in Morrey spaces” [RV1], we claimed the following statement with the name of Theorem 1 —see (5), (6) below for the necessary definiti...

and Applied Analysis 3 In literature, several authors have considered different kinds of weighted spaces of Morrey type and their applications to the study of elliptic equations, both in the degenerate case and in the nondegenerate one see e.g., 9–11 . In this paper, given a weight ρ in a class of measurable functions G Ω see § 6 for its definition , we prove that the corresponding weighted spa...

Abstract We study a characterization of the precompactness sets in variable exponent Morrey spaces on bounded metric measure spaces. Totally are characterized from several points view for case over This is new constant exponents.

We develop a framework for deriving governing partial differential equations for variational problems on spaces of conformal mappings. The main motivation is to obtain differential equations for the conformal motion of free boundary continua, of interest in image and shape registration. A fundamental tool in the paper, the Hodge–Morrey–Friedrichs decompositions of differential forms on manifold...

Our aim in this paper is to establish Hardy-Sobolev inequalities for Sobolev functions and generalized Riesz potentials central Herz-Morrey spaces on the unit ball. As an application, we obtain norm Green potentials.

We give a new proof of the existence ([HM], [Ren]) of a Jenkins-Strebel differential Φ on a Riemann surface R with prescribed heights of cylinders by considering the harmonic map from R to the leaf space of the vertical foliation of Φ, thought of as a Riemannian graph. The novelty of the argument is that it is essentially Riemannian as well as elementary; moreover, the harmonic maps existence t...

In this paper, we prove the boundedness of multilinear Littlewood-Paley square operators and their commutators on weighted Morrey spaces, then give weak-type $$L\log L$$ estimates for g-functions Marcinkiewicz integrals spaces in form corollaries.