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...

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...

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...

Abstract: An affine Moser-Trudinger inequality, which is stronger than the Euclidean MoserTrudinger inequality, is established. In this new affine analytic inequality an affine energy of the gradient replaces the standard L energy of gradient. The geometric inequality at the core of the affine Moser-Trudinger inequality is a recently established affine isoperimetric inequality for convex bodies...

In this article, we will study the boundedness of intrinsic square functions on Morrey-Herz spaces M K q ( · ) , p ? ? ? n ). The commutators generated by B O and is also discussed aforementioned spaces.

In the current paper, we obtain boundedness of a rough p-adic fractional integral operator on central Morrey spaces. Moreover, establish λ-central bounded mean oscillations estimate for commutators

In this paper we define a new class of continuous fractional wavelet transform (CFrWT) and study its properties in Hardy space Morrey space. The theory developed generalize complement some already existing results.