Two power-weight inequalities for the Hilbert transform on the cones of monotone functions

DOI10.1080/17476933.2011.559546zbMath1237.44005OpenAlexW1998054374MaRDI QIDQ3094260

Sergey Yu. Tikhonov, Vladimir D. Stepanov

Publication date: 21 October 2011

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17476933.2011.559546

zbMATH Keywords

Hilbert transformmonotone functionsweighted norm inequalities

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Monotonic functions, generalizations (26A48) Inequalities involving derivatives and differential and integral operators (26D10) Conjugate functions, conjugate series, singular integrals (42A50)

Related Items (6)

On the boundedness of the Hilbert transform from weighted Sobolev space to weighted Lebesgue space ⋮ The weighted inequalities for a certain class of quasilinear integral operators on the cone of monotone functions ⋮ Weight boundedness of a class of quasilinear operators on the cone of monotone functions ⋮ Re-expansions on compact Lie groups ⋮ Weighted Estimates for the Discrete Hilbert Transform ⋮ Reduction theorems for weighted integral inequalities on the cone of monotone functions

Cites Work

• Trigonometric series with general monotone coefficients
• Sharp two-weight inequalities for singular integrals, with applications to the Hilbert transform and the Sarason conjecture
• Some more theorems concerning Fourier series and Fourier power series
• The Fourier Transforms of General Monotone Functions
• Some Theorems on Odd and Even Functions
• Integral Operators on the Cone of Monotone Functions
• Boundedness of Some Integral Operators
• Weighted Hardy Inequalities for Increasing Functions

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