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

BONGIOANNI, BRUNO; CABRAL, ENRIQUE ADRIÁN; HARBOURE, ELEONOR

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 type begin{equation} int_{R^d} |Tf(x)|^p w(x) dx leq C int_{R^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 p in (0,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 Schrödinger semigroup.