Convergence of singular integrals with general measures

• Autores: Pertti Mattila , Joan Verdera
• Localización: Journal of the European Mathematical Society, ISSN 1435-9855, Vol. 11, Nº 2, 2009, págs. 257-271
• Idioma: inglés
• DOI: 10.4171/jems/149
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• Resumen

  • We show that $L^2$-bounded singular integrals in metric spaces with respect to general measures and kernels converge weakly. This implies a kind of average convergence almost everywhere. For measures with zero density we prove the almost everywhere existence of principal values.