"b"-weighted dyadic BMO from dyadic BMO and associated "T(b)" theorems

• Autores: Stephanie Anne Salomone
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 61, Fasc. 2, 2010, págs. 151-171
• Idioma: español
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• Resumen

  • Given a function $b$, and using adapted Haar wavelets, we define a $\BMO$-type norm which is dependent on $b$. In both global and local cases, we find the dependence of the bounds on $\|f\|_{\BMO}$ by the bounds on the $b$-weighted $\BMO$ norm of $f$. We show that the dependence is sharp in the global case. Multiscale analysis is used in the local case. We formulate as corollaries global and local dyadic $T(b)$ theorems whose hypotheses include a bound on the $b$-weighted $\BMO$-norm of $T^*(1)$.