L2-boundedness of a singular integral operator

• Autores: Yibiao Pan, Dashan Fan
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 41, Nº 2, 1997, págs. 317-333
• Idioma: inglés
• DOI: 10.5565/publmat_41297_01
• Títulos paralelos:
  • Acotabilidad L2 de un operador integral singular
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• Resumen

  • In this paper we study a singular integral operator $T$ with rough kernel. This operator has singularity along sets of the form $\{x=Q(|y|)y'\}$, where $Q(t)$ is a polynomial satisfying $Q(0)=0$. We prove that $T$ is a bounded operator in the space $L^2(R^n)$, $n\ge 2$, and this bound is independent of the coefficients of $Q(t)$.

    We also obtain certain Hardy type inequalities related to this operator.