@article{article_1030942, title={A different approach to boundedness of the B-maximal operators on the variable Lebesgue spaces}, journal={Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics}, volume={71}, pages={710–719}, year={2022}, DOI={10.31801/cfsuasmas.1030942}, author={Kaya, Esra}, keywords={Maximal operator, singular integrals, variable Lebesgue space}, abstract={By using the <span class="MathJax_Preview" style="color:inherit;"> </span> <span class="mjx-chtml MathJax_CHTML" style="font-size:123%;"> <span class="mjx-math"> <span class="mjx-mrow"> <span class="mjx-msubsup"> <span class="mjx-base"> <span class="mjx-mi"> <span class="mjx-char MJXc-TeX-math-I" style="padding-top:.441em;padding-bottom:.253em;">L </span> </span> </span> <span class="mjx-sub" style="font-size:70.7%;vertical-align:-.275em;padding-right:.071em;"> <span class="mjx-texatom"> <span class="mjx-mrow"> <span class="mjx-mi"> <span class="mjx-char MJXc-TeX-math-I" style="padding-top:.191em;padding-bottom:.441em;">p </span> </span> <span class="mjx-mo"> <span class="mjx-char MJXc-TeX-main-R" style="padding-top:.441em;padding-bottom:.566em;">( </span> </span> <span class="mjx-mo"> <span class="mjx-char MJXc-TeX-main-R" style="padding-top:.003em;padding-bottom:.316em;">⋅ </span> </span> <span class="mjx-mo"> <span class="mjx-char MJXc-TeX-main-R" style="padding-top:.441em;padding-bottom:.566em;">) </span> </span> </span> </span> </span> </span> <span class="mjx-mo"> <span class="mjx-char MJXc-TeX-main-R" style="padding-top:.316em;padding-bottom:.441em;">− </span> </span> </span> </span> <span class="MJX_Assistive_MathML">Lp(⋅)− </span> </span>boundedness of a maximal operator defined on homogeneous space, it has been shown that the <span class="MathJax_Preview" style="color:inherit;"> </span> <span class="mjx-chtml MathJax_CHTML" style="font-size:123%;"> <span class="mjx-math"> <span class="mjx-mrow"> <span class="mjx-mi"> <span class="mjx-char MJXc-TeX-math-I" style="padding-top:.441em;padding-bottom:.253em;">B </span> </span> <span class="mjx-mo"> <span class="mjx-char MJXc-TeX-main-R" style="padding-top:.316em;padding-bottom:.441em;">− </span> </span> </span> </span> <span class="MJX_Assistive_MathML">B− </span> </span>maximal operator is bounded. In the present paper, we aim to bring a different approach to the boundedness of the <span class="MathJax_Preview" style="color:inherit;"> </span> <span class="mjx-chtml MathJax_CHTML" style="font-size:123%;"> <span class="mjx-math"> <span class="mjx-mrow"> <span class="mjx-mi"> <span class="mjx-char MJXc-TeX-math-I" style="padding-top:.441em;padding-bottom:.253em;">B </span> </span> <span class="mjx-mo"> <span class="mjx-char MJXc-TeX-main-R" style="padding-top:.316em;padding-bottom:.441em;">− </span> </span> </span> </span> <span class="MJX_Assistive_MathML">B− </span> </span>maximal operator generated by generalized translation operator under a continuity assumption on <span class="MathJax_Preview" style="color:inherit;"> </span> <span class="mjx-chtml MathJax_CHTML" style="font-size:123%;"> <span class="mjx-math"> <span class="mjx-mrow"> <span class="mjx-mi"> <span class="mjx-char MJXc-TeX-math-I" style="padding-top:.191em;padding-bottom:.441em;">p </span> </span> <span class="mjx-mo"> <span class="mjx-char MJXc-TeX-main-R" style="padding-top:.441em;padding-bottom:.566em;">( </span> </span> <span class="mjx-mo"> <span class="mjx-char MJXc-TeX-main-R" style="padding-top:.003em;padding-bottom:.316em;">⋅ </span> </span> <span class="mjx-mo"> <span class="mjx-char MJXc-TeX-main-R" style="padding-top:.441em;padding-bottom:.566em;">) </span> </span> </span> </span> <span class="MJX_Assistive_MathML">p(⋅) </span> </span>. It is noteworthy to mention that our assumption is weaker than uniform Hölder continuity.}, number={3}, publisher={Ankara University}