Integral Properties of Generalized Potentials of the Type Besseland Riesz Type

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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.

About the authors

Kh Almohammad

Department of Nonlinear Analysis and Optimization Peoples’ Friendship University of Russia (RUDN university)

Author for correspondence.
Email: khaleel.almahamad1985@gmail.com

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

6, Miklukho-Maklaya St., Moscow, 117198, Russian Federation

N Kh Alkhalil

Department of Nonlinear Analysis and Optimization Peoples’ Friendship University of Russia (RUDN university)

Email: khaleel.almahamad1985@gmail.com

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

6, Miklukho-Maklaya St., Moscow, 117198, Russian Federation

References

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

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