Fractional Integrals And RIESZ Transform acting on certain LIPSCHITZ Spaces

Abstract

We make a unifying approach to the study of mapping properties of fractional integrals and Riesz transforms acting on spaces of functions f verifying sup B (1 w(a, r) 1 |B| ˆ B |f − mBf| q 1/q )< ∞ , where w is a non negative functional defined on the family of balls B ⊂ Rn with center a and radius r. So, at the same time, we are able to treat such cases as BMO, Lipschitz spaces and spaces of functions with variable smoothness among others. Results about pointwise smoothness related to these spaces are included as well.