LINEAR TRUNCATIONS OF THE HILBERT TRANSFORM
Copyright policy )LINEAR TRUNCATIONS OF THE HILBERT TRANSFORM
The author considers the operator \(H_{a,b,c,d}f(x)=\int_{ax+b}^{cx+d} dt/t\) arising in connection with questions about bilinear operators of type \(\int_{R^1}g(t-ax)f(x-t) dt/t\), generalizing the Hilbert transform, but for \(a\neq 0\) being no convolutions. The following problems are studied here: 1) Boundedness of \(H_{a,b,c,d}:L^p\to L^q\) and an estimate for its norm, \(a\neq 0\), \(1
truncation, Singular and oscillatory integrals (Calderón-Zygmund, etc.), Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, Conjugate functions, conjugate series, singular integrals, Special integral transforms (Legendre, Hilbert, etc.), 42B20, linear truncations, Hilbert transform
truncation, Singular and oscillatory integrals (Calderón-Zygmund, etc.), Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, Conjugate functions, conjugate series, singular integrals, Special integral transforms (Legendre, Hilbert, etc.), 42B20, linear truncations, Hilbert transform
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