The ε-maximal operator and Haar multipliers on variable Lebesgue spaces

Abstract

Recently, Stockdale, Villarroya, and Wick introduced the ε -maximal operator to prove the Haar multiplier is bounded on the weighted spaces L p (w) for a class of weights larger than A p .We prove the ε -maximal operator and Haar multiplier are bounded on variable Lebesgue spaces L p(•) (R n ) for a larger collection of exponent functions than the log-Hölder continuous functions used to prove the boundedness of the maximal operator on L p(•) (R n ) .We also prove that the Haar multiplier is compact when restricted to a dyadic cube Q 0 .

Locations

• Mathematical Inequalities & Applications - View - PDF