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

• Autores: Pascal Auscher, José María Martell Berrocal
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 212, Nº 1, 2007, págs. 225-276
• Idioma: inglés
• DOI: 10.1016/j.aim.2006.10.002
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• Resumen

  • 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