Two-Weighted Inequalities for the Riesz Potential in p-Convex Weighted Modular Banach Function Spaces

WOS: 000435418800001We prove the property of two-weight boundedness for the Riesz potential from one weighted Banach function space to another weighted Banach function space. In particular, we establish the two-weight boundedness for the Riesz potential and determine sufficient conditions on weights for the boundedness of the Riesz potential in weighted Musielak-Orlicz spaces.Science Development Foundation [EIF-2013-9(15)-46/10/1]; Presidium of Azerbaijan National Academy of ScienceAzerbaijan National Academy of Sciences (ANAS)The research of R. A. Bandaliyev and V. S. Guliyev was partially supported by the Science Development Foundation under President of the Republic of Azerbaijan, Grant EIF-2013-9(15)-46/10/1 and by the grant of the Presidium of Azerbaijan National Academy of Science (2015)

The optimal control problem in the processes described by the Goursat problem for a hyperbolic equation in variable exponent Sobolev spaces with dominating mixed derivatives

WOS: 000376798700002In this paper a necessary and sufficient condition, such as the Pontryagin's maximum principle for an optimal control problem with distributed parameters, is given by a hyperbolic equation of the second order with L-p(x)-coefficients. The results can be used in the theory of optimal processes for distribution Pontryagin maximum principle for various controlled processes described by hyperbolic equations of second order with discontinuous coefficients in variable exponent Sobolev spaces with dominant mixed derivatives. (C) 2016 Elsevier B.V. All rights reserved.Presidium Azerbaijan National Academy of ScienceAzerbaijan National Academy of Sciences (ANAS)The authors would like to express their gratitude to the referee for his/her very valuable comments and suggestions. The research of R. Bandaliyev and V. Guliyev was partially supported by the grant of Presidium Azerbaijan National Academy of Science 2015