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oai:bayburt-rdlopen.rawdatalibrary.net:bayburt/132342026-10-29T19:52:12Zopenairedrivercom_bayburt_10000col_bayburt_10001com_bayburt_10007col_bayburt_10218

Approximating Functions in the Power-Type Weighted Variable Exponent Sobolev Space by the Hardy Averaging OperatorAyazoglu, RabilEkincioglu, IsmailŞener, S. ŞuleApproximationHardy averaging operatorPower-type weighted grand Lebesgue spaces with variable exponentPower-type weighted Sobolev spaces with variable exponentWe investigate the problem of approximating function f in the power-type weighted variable exponent Sobolev space (Formula presented), by the Hardy averaging operator (Formula presented). If α(.) x 0 the function f lies in the power-type weighted variable exponent Sobolev space (Formula presented) (0, 1), it is shown that (Formula presented), where C is a positive constant. Moreover, we consider the problem of boundedness of Hardy averaging operator A in power-type weighted variable exponent grand Lebesgue spaces (Formula presented) (0, 1). The sufficient α(.) criterion established on the power-type weight function α(.) and exponent p(.) for the Hardy averaging operator to be bounded in these spaces.University of Nis2022Articlehttps://rdlopen.rawdatalibrary.net/r/bayburt/13234https://doi.org/10.2298/fil2210321a0354-5180enFilomatinfo:eu-repo/semantics/openAccessinfo:eu-repo/semantics/articlehttps://bayburt-rdlopen.rawdatalibrary.net/tr/items/bayburt/13234