On the local properties of exponent for boundedness of Hardy-Littlewood maximal operator in variable Lebesgue spaces

Author: Shalva Zviadadze
Co-authors: Tengiz Kopaliani
Annotation:

In the talk the answer is given to the question asked in the David Cruz-Uribe and Alberto Fiorenza’s monograph. The question is about local properties of exponent for the boundedness of Hardy-Littlewood maximal operator in variable Lebesgue space. Particularly, an example is constructed, that proves the hypothesis stated in the monograph is wrong.