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

• Autorzy: Yuichi Kanjin
• Języki publikacji: EN

Abstrakty

EN

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 $H^{p}(ℝ)$.

Kategorie tematyczne

• 47B38: Operators on function spaces (general)
• 42B30: H p -spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2001
• Tom: 148
• Numer: 1
• Strony: 37-45

Daty

wydano

2001

Twórcy

autor

Yuichi Kanjin

• Department of Mathematics, General Education Hall, Kanazawa University, Kanazawa 920-1192, Japan

Identyfikatory

DOI

10.4064/sm148-1-4