A generalized Kolmogorov inequality for the Hilbert transform

Mark A. Pinsky*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

If f ∈ L1(R1; (1 + |x|)-1dx) we can define the Hilbert transform H f almost everywhere (Lebesgue) and obtain an estimate for μ{x : |H f(x)| ≥ α} where μ is a suitable finite measure. The classical Kolmogorov inequality for the Lebesgue measure of {x: |H f(x) | ≥ α} is obtained by a scaling argument.

Original languageEnglish (US)
Pages (from-to)753-758
Number of pages6
JournalProceedings of the American Mathematical Society
Volume130
Issue number3
DOIs
StatePublished - 2002

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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