Fractional Integral and Riesz Transform acting on Certain Lipschitz Spaces

MAURICIO RAMSEYER; OSCAR SALINAS; BEATRIZ VIVIANI

MICHIGAN MATHEMATICAL JOURNAL

MICHIGAN MATHEMATICAL JOURNAL

Año: 2016 vol. 65 p. 35 - 56

0026-2285

We make a unifying approach to the studyof mapping properties of fractional integralsand Riesz transforms acting on spacesof functions $f$ verifying[ sup_B left( rac1{w(a,r)}left( rac1{|B|} int_B |f-m_Bf|^qight)^{1/q}ight) < infty,, ]where $w$ is a non negative functional definedon the family of balls $B subset Real^n$ withcenter $a$ and radius $r$. So, at the same time, we are able to treatsuch cases as BMO, Lipschitz spaces and spacesof functions with variable smoothness among others.Results about pointwise smoothness related tothese spaces are included as well.