Hardy Spaces with Variable Exponents

Abstract

In this paper, we gather the essential contents of the talk ?Hardy spaces with variable exponents given by the second author at the CIMPA2017 Research School-IXEscuela Santaló Harmonic Analysis, Geometric Measure Theory and Applications,which took place in Buenos Aires, Argentina, from July 31 to August 11, 2017. Wegive an overview of the latest advances about Hardy and local Hardy spaces withvariable exponents in different contexts. We cannot be exhaustive and we recommendthe interested reader to consult the references at the end of this paper and others that can be found in them.