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Transplantation operators and Cesàro operators for the Hankel transform

100%

Kanjin Y.

Studia Mathematica

2006

tom 174

nr 1

29-45

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.

The Hausdorff operators on the real Hardy spaces $H^{p}(ℝ)$

100%

Kanjin Y.

Studia Mathematica

2001

tom 148

nr 1

37-45

We prove that the Hausdorff operator generated by a function ϕ is bounded on the real Hardy space $H^{p}(ℝ)$, 0 < p ≤ 1, if the Fourier transform ϕ̂ of ϕ satisfies certain smoothness conditions. As a special case, we obtain the boundedness of the Cesàro operator of order α on $H^{p}(ℝ)$, 2/(2α+1) < p ≤ 1. Our proof is based on the atomic decomposition and molecular characterization of $H^{p}(ℝ)$.

Ograniczanie wyników

2 Studia Mathematica

2 Kanjin Y.

1 2006

1 2001

Wyniki wyszukiwania

Transplantation operators and Cesàro operators for the Hankel transform

The Hausdorff operators on the real Hardy spaces $H^{p}(ℝ)$