Lerner's inequality associated to a critical radius function and applications

BONGIOANNI, CABRAL, HARBOURE

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

ACADEMIC PRESS INC ELSEVIER SCIENCE

Lugar: Amsterdam; Año: 2013 vol. 407 p. 35 - 55

0022-247X

This work deals with weighted inequalities of the typebegin{equation*}int_{Br^d} |Tf(x)|^p w(x) dx leq C int_{Br^d} |Sf(x)|^p w(x) dx,end{equation*}where $S$ is some maximal operator and $T$ is an operator that comes from the harmonic analysis associated to a critical radius function. The weight $w$ belongs to an appropriate family and $0<p<infty$. The proofs are based on an adapted Lerner´s inequality and some point-wise estimates. The results can be applied to obtain inequalities for several operators associated to the Schr"odinger semigroup.