Resumen de Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part I: General operator theory and weights

Pascal Auscher, José María Martell Berrocal

• This is the first part of a series of four articles. In this work, we are interested in weighted norm estimates. We put the emphasis on two results of different nature: one is based on a good-? inequality with two parameters and the other uses Calderón¿Zygmund decomposition. These results apply well to singular ¿non-integral¿ operators and their commutators with bounded mean oscillation functions. Singular means that they are of order 0, ¿non-integral¿ that they do not have an integral representation by a kernel with size estimates, even rough, so that they may not be bounded on all Lp spaces for 1