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In this note we present a simple proof of a recent result of Mattila and Melnikov on the existence of limε→0 ∫|ζ-z|>ε (ζ - z)-1dμ(ζ) for finite Borel measures μ in the plane.
Verdera, Joan. "A weak type inequality for Cauchy transforms of finite measures.." Publicacions Matemàtiques 36.2B (1992): 1029-1034. <http://eudml.org/doc/41767>.
@article{Verdera1992, abstract = {In this note we present a simple proof of a recent result of Mattila and Melnikov on the existence of limε→0 ∫|ζ-z|>ε (ζ - z)-1dμ(ζ) for finite Borel measures μ in the plane.}, author = {Verdera, Joan}, journal = {Publicacions Matemàtiques}, keywords = {Cauchy transform; weak type inequality}, language = {eng}, number = {2B}, pages = {1029-1034}, title = {A weak type inequality for Cauchy transforms of finite measures.}, url = {http://eudml.org/doc/41767}, volume = {36}, year = {1992}, }
TY - JOUR AU - Verdera, Joan TI - A weak type inequality for Cauchy transforms of finite measures. JO - Publicacions Matemàtiques PY - 1992 VL - 36 IS - 2B SP - 1029 EP - 1034 AB - In this note we present a simple proof of a recent result of Mattila and Melnikov on the existence of limε→0 ∫|ζ-z|>ε (ζ - z)-1dμ(ζ) for finite Borel measures μ in the plane. LA - eng KW - Cauchy transform; weak type inequality UR - http://eudml.org/doc/41767 ER -