Multiplier transformations on $H^{p}$ spaces

• Autorzy: Daning Chen , Dashan Fan
• Języki publikacji: EN

Abstrakty

EN

The authors obtain some multiplier theorems on $H^p$ spaces analogous to the classical $L^p$ multiplier theorems of de Leeuw. The main result is that a multiplier operator $(Tf)^(x) = λ(x)f̂(x)$ $(λ ∈ C(ℝ^n))$ is bounded on $H^p(ℝ^n)$ if and only if the restriction ${λ(εm)}_{m∈Λ}$ is an $H^p(T^n)$ bounded multiplier uniformly for ε>0, where Λ is the integer lattice in $ℝ^n$.

Kategorie tematyczne

• 42B15: Multipliers
• 42B30: H p -spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 131
• Numer: 2
• Strony: 189-204

Daty

wydano

1998

otrzymano

1998-04-17

Twórcy

autor

Daning Chen

• Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201, U.S.A.

autor

Dashan Fan

• Department of Mathematical Sciences University of Wisconsin-Milwaukee Milwaukee, Wisconsin 53201, U.S.A.,

Bibliografia

• [1] P. Auscher and M. J. Carro, On relations between operators on $ℝ^n$, $T^n$ and $ℤ^n$, Studia Math. 101 (1990), 165-182.
• [2] D. Chen, Multipliers on certain function spaces, Ph.D. thesis, Univ. of Wisconsin-Milwaukee, 1998.
• [3] D. Fan, Hardy spaces on compact Lie groups, Ph.D. thesis, Washington University, St. Louis, 1990.
• [4] C. Fefferman and E. M. Stein, $H^p$ spaces of several variables, Acta Math. 129 (1972), 137-193.
• [5] D. Goldberg, A local version of real Hardy spaces, ibid. 46 (1979), 27-42.
• [6] C. Kenig and P. Thomas, Maximal operators defined by Fourier multipliers, Studia Math. 68 (1980), 79-83.
• [7] S. Krantz, Fractional integration on Hardy spaces, ibid. 73 (1982), 87-94.
• [8] K. de Leeuw, On $L_p$ multipliers, Ann. of Math. 91 (1965), 364-379.
• [9] E. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, 1971.