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Öğe Hardy's inequality in power-type weighted LP(•) (0, ?) spaces(Academic Press Inc Elsevier Science, 2007) Mashiyev, R. A.; Cekic, B.; Mamedov, F. I.; Ogras, S.In this article, our aim is to prove Hardy's inequality in power-type weighted L-p(.) (0, infinity) spaces by obtaining regularity condition on the exponents p(.), q(.) and alpha(.) defined at every point of the domain of test function with u(0) = 0 (or vanishing at infinity) under the log-Holder continuity conditions at the origin and infinity. (c) 2006 Elsevier Inc. All rights reserved.Öğe ON SOME NONUNIFORM CASES OF THE WEIGHTED SOBOLEV AND POINCARE INEQUALITIES(Amer Mathematical Soc, 2009) Mamedov, F. I.; Amanov, R. A.Weighted inequalities parallel to f parallel to(q,nu,B0) <= C Sigma(n)(j=1) parallel to f(xj)parallel to(p,omega j,B0) of Sobolev type (supp f subset of B-0) and of Poincare type ((f) over bar (nu,B0) = 0) are studied, with different weight functions for each partial derivative f(xj), for parallelepipeds B-0 subset of E-n, n >= 1. Also, weighted inequalities parallel to f parallel to(q,nu) <= C parallel to X f parallel to(p,omega) of the same type are considered for vector fields X = {X-j}, j = 1,..., m, with infinitely differentiable coefficients satisfying the Hormander condition.Öğe On the behavior of solutions of some nonlinear degenerate elliptic inequalities(Maik Nauka/Interperiodica/Springer, 2010) Mamedov, F. I.; Ibragimov, T. T.We consider the behavior of solutions in unbounded domains as |x| -> a and in a neighborhood of an isolated singular point for a class of nonlinear elliptic equations and inequalities degenerating with respect to the coordinate variable, the solution, and the solution gradient.Öğe Regularity of the solutions of degenerate elliptic equations in divergent form(Maik Nauka/Interperiodica/Springer, 2008) Amanov, R. A.; Mamedov, F. I.A priori estimates of the solution to the Dirichlet problem and of its first derivatives in terms of weighted Lebesgue norms are obtained for linear and quasilinear equations with degeneracy from A(p) Muckenhoupt classes.Öğe Two-weight inequalities for the maximal operator in a Lebesgue space with variable exponent(2011) Mamedov, F. I.; Zeren, Yusuf; 0000-0003-1999-3279; 0000-0001-8346-2208We study a two-weight problem for the Hardy-Littlewood maximal operator in variable exponent Lebesgue spaces Lp(·). The exponential function satisfies some logarithmic type continuity conditions. Bibliography: 25 titles.