Integral Properties of Generalized Potentials of the Type Besseland Riesz Type

Cover Page

Abstract


In the paper we study integral properties of convolutions of functions with kernels generalizingthe classical Bessel-Macdonald kernels (), ∈ , 0 < < . The local behavior of Bessel-Macdonald kernels in the neighborhood of the origin are characterized by the singularity ofpower type ||-. The kernels of generalized Bessel-Riesz potentials may have non-powersingularities in the neighborhood of the origin. Their behavior at the infinity is restricted onlyby the integrability condition, so that the kernels with compact support are included too. In thepaper the general criteria for the embedding of potentials into rearrangement invariant spacesare concretized in the case when the basic space coincides with the weighted Lorentz space.We obtain the explicit descriptions for the optimal rearrangement invariant space for such anembedding.


Kh Almohammad

Principal contact for editorial correspondence.
khaleel.almahamad1985@gmail.com
Department of Nonlinear Analysis and Optimization Peoples’ Friendship University of Russia (RUDN university) 6, Miklukho-Maklaya St., Moscow, 117198, Russian Federation

Almohammad Kh. - student of Nonlinear Analysis and Optimization Department of Peoples’ Friendship University of Russia (RUDN University)

N Kh Alkhalil

khaleel.almahamad1985@gmail.com
Department of Nonlinear Analysis and Optimization Peoples’ Friendship University of Russia (RUDN university) 6, Miklukho-Maklaya St., Moscow, 117198, Russian Federation

Alkhalil N. - student of Nonlinear Analysis and Optimization Department of Peoples’ Friendship University of Russia (RUDN University)

  • R. O’Neil, Convolution Operators and
  • M.L. Goldman, On the Cones of Rearrangements for Generalized Bessel and Riesz Potentials, Complex Variables and Elliptic Equations.
  • Yu.V. Netrusov, Embedding Theorems of Lizorkin–Triebel Spaces, Notes of scientific seminars LOMI 159 (1987) 103–112, in Russian.
  • Yu.V. Netrusov, Embedding Theorems of Besov Spaces into Ideal Spaces, Notes of scientific seminars LOMI 159 (1987) 69–82, in Russian.
  • M.L. Goldman, F. Henriques, Description of Rearrangement Invariant Shell of an Anisotropic Calderon Space, Proceedings of the Steklov Institute of Mathematics 248 (2005) 94–105, in Russian.
  • M.L. Goldman, On Optimal Investment Potentials of the Generalized Bessel and Riesz, Proceedings of the Steklov Institute of Mathematics 269 (2010) 91–111, in Russian.
  • A. Gogatishvili, M. Johansson, C.A. Okpoti, L. E. Persson, Characterization of Embeddings in Lorentz Spaces Using a Method of Discretization and Anti- Discretization, Bulletin of the Australian Mathematical Society 76 (2007) 69–92.
  • V.G. Mazya, Sobolev Spaces, Publishing house Leningrad state University, Leningrad, 1985, in Russian.
  • A.V. Malysheva, Optimal Embedding of the Generalized Riesz Potentials, Bulletin of Peoples’ Friendship University of Russia. Series: Mathematics. Information Sciences. Physics (2) (2013) 28–37, in Russian.

Views

Abstract - 35

PDF (Russian) - 7


Copyright (c) 2017 Almohammad K., Alkhalil N.K.

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.