The Complete (L..., L...) Mapping Properties for a Class of Oscillatory Integrals.
The conjugation operator on .
The Muckenhoupt class A₁(R)
It is shown that the Muckenhoupt structure constants for f and f* on the real line are the same.
The spectral decomposition of weighted shifts and the condition
The Stein-Weiss theorem for the ergodic Hilbert transform
The Stein-Weiss theorem that the distribution function of the Hilbert transform of the characteristic function of E depends only on the measure of E is generalized for the ergodic Hilbert transform in the case of a one-parameter flow of measure-preserving transformations on a σ-finite measure space.
Transplantation operators and Cesàro operators for the Hankel transform
The transplantation operators for the Hankel transform are considered. We prove that the transplantation operator maps an integrable function under certain conditions to an integrable function. As an application, we obtain the L¹-boundedness and H¹-boundedness of Cesàro operators for the Hankel transform.