Characterizations of localized BMO(R^n) via commutators of localized Riesz transforms and fractional integrals associated to Schrödinger operators

• Autores: Dachun Yang, Dongyong Yang
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 61, Fasc. 1, 2010, págs. 65-79
• Idioma: inglés
• DOI: 10.1007/bf03191227
• Enlaces
  • Texto completo
• Resumen

  • Let ${\mathcal L}\equiv-\Delta+V$ be the Schr\"odinger operator in ${\mathbb R^n}$, where $V$ is a nonnegative function satisfying the reverse H\"older inequality. Let $\rho$ be an admissible function modeled on the known auxiliary function determined by $V$. In this paper, the authors establish several characterizations of the space ${\mathop\mathrm{BMO_\rho(\rn)}}$ in terms of commutators of several different localized operators associated to $\rho$, respectively; these localized operators include localized Riesz transforms and their adjoint operators, the localized fractional integral and its adjoint operator, the localized fractional maximal operator and the localized Hardy-Littlewood-type maximal operator.

    These results are new even for the space ${\mathop\mathrm{BMO_{\mathcal L}(\rn)}}$ introduced by J. Dziuba\'nski, G. Garrig\'os et al.

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