A different approach to boundedness of the B-maximal operators on the variable Lebesgue spaces

Kaya, ESRA

doi:10.31801/cfsuasmas.1030942

A different approach to boundedness of the B-maximal operators on the variable Lebesgue spaces

Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics, cilt.71, sa.3, ss.710-719, 2022 (Hakemli Dergi)

Yayın Türü: Makale / Tam Makale
Cilt numarası: 71 Sayı: 3
Basım Tarihi: 2022
Doi Numarası: 10.31801/cfsuasmas.1030942
Dergi Adı: Communications Faculty of Sciences University of Ankara Series A1: Mathematics and Statistics
Sayfa Sayıları: ss.710-719
Bilecik Şeyh Edebali Üniversitesi Adresli: Evet

Özet

By using the Lp(⋅)−Lp(⋅)−boundedness of a maximal operator defined on homogeneous space, it has been shown that the B−B−maximal operator is bounded. In the present paper, we aim to bring a different approach to the boundedness of the B−B−maximal operator generated by generalized translation operator under a continuity assumption on p(⋅)p(⋅). It is noteworthy to mention that our assumption is weaker than uniform Hölder continuity.