Continuous characterization of Besov spaces of variable smoothness and integrability

Douadi Drihem, Salah Ben Mahmoud

Published 2018-10-09Version 1

In this paper the authors obtain a new equivalent norms of the Besov spaces of variable smoothness and integrability. Our main tools are the continuous version of Calderon reproducing formula, maximal inequalities and variable exponent technique, but allowing the parameters to vary from point to point will raise extra difficulties which, in general, are overcome by imposing regularity assumptions on these exponents.