High Order Riesz Transforms and Mean Value Formula for Generalized Translate Operator

In this paper, the mean value formula depends on the Bessel generalized shift operator corresponding to the solutions of the boundary value problem related to the Bessel operator are studied. In addition to, Riesz Bessel transforms related to the Bessel operators are studied. Since Bessel generalized shift operator is translation operator corresponding to the Bessel operator, we construct a family of RBxj by using Bessel generalized shift operator. Finally, we analysis weighted inequalities involving Riesz Bessel transforms

Fractional weighted spherical mean and maximal inequality for the weighted spherical mean and its application to singular PDE

In this paper we establish a mean value property for the functions which is satisfied to Laplace-Bessel equation. Our results involve the generalized divergence theorem and the second Green’s identities relating the bulk with the boundary of a region on which differential Bessel operators ac

Theory of generalized Bessel potential space and functional completion

The articles objective is to present norms based on weighted Dirichlet integrals in the space of generalized Bessel potential

Electrorheological Fluids Equations Involving Variable Exponent with Dependence on the Gradient via Mountain Pass Techniques

This article deals with a quasilinear elliptic equation with variable exponent under a homogenous Dirichlet boundary-value condition, where nonlinearity also depends on the gradient of the solution. By using an iterative method based on Mountain Pass techniques, the existence of a positive solution is obtained. © 2016, Copyright © Taylor & Francis Group, LLC

CHARACTERIZATIONS FOR THE FRACTIONAL INTEGRAL OPERATOR AND ITS COMMUTATORS IN GENERALIZED WEIGHTED MORREY SPACES ON CARNOT GROUPS

In this paper, we shall give a characterization for the strong and weak type Spanne type boundedness of the fractional integral operator I-alpha, 0 < alpha < Q on Carrot group G on generalized weighted Morrey spaces M-p,M-phi (G,w), respectively, where Q is the homogeneous dimension of G. Also we give a characterization for the Spanne type boundedness of the commutator operator [b,I-alpha] on generalized weighted Morrey spaces. As applications of the properties of the fundamental solution of sub-Laplacian L on G, we prove two Sobolev-Stein embedding theorems on generalized weighted Morrey spaces in the Carrot group setting

Existence of one weak solution for p(X)-biharmonic equations involving a concave-convex nonlinearity

In the present paper, using variational approach and the theory of the variable exponent Lebesgue spaces, the existence of nontrivial weak solutions to a fourth order elliptic equation involving a p(x)-biharmonic operator and a concave-convex nonlinearity the Navier boundary conditions is obtained. © 2017, Drustvo Matematicara Srbije. All rights reserved

Multiple small solutions for p(x)-Schrödinger equations with local sublinear nonlinearities via genus theory

In this paper, we deal with the following p(x)-Schrödinger problem: (Formula Presented) where the nonlinearity is sublinear. We present the existence of infinitely many solutions for the problem. The main tool used here is a variational method and Krasnoselskii’s genus theory combined with the theory of variable exponent Sobolev spaces. We also establish a Bartsch-Wang type compact embedding theorem for the variable exponent spaces. © 2017, University of Szeged. All rights reserved

Boundedness of the anisotropic fractional maximal operator in anisotropic local Morrey-type spaces

In this paper we study the boundedness of the anisotropic fractional maximal operator in anisotropic local Morrey-type spaces. We reduce this problem to the problem of boundedness of the supremal operator in weighted Lp - spaces on the cone of non-negative non-decreasing functions. This makes it possible to derive sharp sufficient conditions for boundedness for all admissible values of the numerical parameters, which, for a certain range of the numerical parameters, coincide with the necessary ones