Mamedov, Farman I.Harman, Aziz2024-04-242024-04-2420090022-247X1096-0813https://doi.org/10.1016/j.jmaa.2008.12.029https://hdl.handle.net/11468/15668The boundedness of Hardy type operator Hf (x) = integral((t is an element of R)n(:) (vertical bar t vertical bar <=vertical bar x vertical bar)) f(t)dt is studied in weighted variable exponent Lebesgue spaces L-p(.). The necessary and sufficient criterion established on the weight functions v(x), omega(x) and exponents p(x). q(x) for the Hardy operator to be bounded from L-p(.)(omega) to L-q(.)(v). The exponents satisfy a modified logarithmic condition near zero and at infinity: there exists delta > 0, there exists integral(infinity), there exists f(0) is an element of R sup(x is an element of B(o,delta)) vertical bar f(x) - f (0)vertical bar In I/W(x) < infinity: there exists N > 1 sup(x is an element of R)n(\B(0,N)) vertical bar f(x) - f(infinity)vertical bar In W(x) < infinity, where W(x) = integral({t is an element of R)n(:) (vertical bar t vertical bar <=vertical bar x vertical bar})omega(-1/(p(t)-1))(t)dt. (C) 2008 Elsevier Inc. All rights reserved.eninfo:eu-repo/semantics/closedAccessHardy OperatorHardy InequalityVariable ExponentsWeighted InequalityArticle3532521530WOS:0002652249000052-s2.0-5854910247110.1016/j.jmaa.2008.12.029Q2Q1