# Transference and restriction of maximal multiplier operators on Hardy spaces

Studia Mathematica (1993)

- Volume: 105, Issue: 2, page 121-134
- ISSN: 0039-3223

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topLiu, Zhixin, and Lu, Shanzhen. "Transference and restriction of maximal multiplier operators on Hardy spaces." Studia Mathematica 105.2 (1993): 121-134. <http://eudml.org/doc/215988>.

@article{Liu1993,

abstract = {The aim of this paper is to establish transference and restriction theorems for maximal operators defined by multipliers on the Hardy spaces $H^p(ℝ^n)$ and $H^p(^n)$, 0 < p ≤ 1, which generalize the results of Kenig-Tomas for the case p > 1. We prove that under a mild regulation condition, an $L^∞(ℝ^n)$ function m is a maximal multiplier on $H^p(ℝ^n)$ if and only if it is a maximal multiplier on $H^p(^n)$. As an application, the restriction of maximal multipliers to lower dimensional Hardy spaces is considered.},

author = {Liu, Zhixin, Lu, Shanzhen},

journal = {Studia Mathematica},

keywords = {transference; restriction; maximal operators; Hardy spaces; maximal multiplier},

language = {eng},

number = {2},

pages = {121-134},

title = {Transference and restriction of maximal multiplier operators on Hardy spaces},

url = {http://eudml.org/doc/215988},

volume = {105},

year = {1993},

}

TY - JOUR

AU - Liu, Zhixin

AU - Lu, Shanzhen

TI - Transference and restriction of maximal multiplier operators on Hardy spaces

JO - Studia Mathematica

PY - 1993

VL - 105

IS - 2

SP - 121

EP - 134

AB - The aim of this paper is to establish transference and restriction theorems for maximal operators defined by multipliers on the Hardy spaces $H^p(ℝ^n)$ and $H^p(^n)$, 0 < p ≤ 1, which generalize the results of Kenig-Tomas for the case p > 1. We prove that under a mild regulation condition, an $L^∞(ℝ^n)$ function m is a maximal multiplier on $H^p(ℝ^n)$ if and only if it is a maximal multiplier on $H^p(^n)$. As an application, the restriction of maximal multipliers to lower dimensional Hardy spaces is considered.

LA - eng

KW - transference; restriction; maximal operators; Hardy spaces; maximal multiplier

UR - http://eudml.org/doc/215988

ER -

## References

top- [1] E. Berkson, T. A. Gillespie and P. S. Muhly, ${L}^{p}$-Multiplier transference induced by representations in Hilbert space, Studia Math. 94 (1989), 51-61. Zbl0722.43001
- [2] R. R. Coifman and G. Weiss, Transference Methods in Analysis, CBMS Regional Conf. Ser. in Math. 31, Amer. Math. Soc., Providence, R.I., 1977. Zbl0371.43009
- [3] C. Fefferman and E. M. Stein, ${H}^{p}$ spaces of several variables, Acta Math. 129 (1972), 137-193. Zbl0257.46078
- [4] M. Frazier and B. Jawerth, Decomposition of Besov spaces, Indiana Univ. Math. J. 34 (1985), 777-799. Zbl0551.46018
- [5] C. E. Kenig and P. A. Tomas, Maximal operators defined by Fourier multipliers, Studia Math. 68 (1980), 79-83. Zbl0442.42013
- [6] K. de Leeuw, On ${L}_{p}$ multipliers, Ann. of Math. 81 (1965), 364-379.
- [7] Z. X. Liu, Multipliers on real Hardy spaces, Scientia in China (Ser. A) 35 (1992), 55-69.
- [8] C. Meaney, Transferring estimates for zonal convolution operators, Anal. Math. 15 (1989), 175-193. Zbl0694.43004
- [9] A. Miyachi, On some Fourier multipliers for ${H}^{p}\left({\mathbb{R}}^{n}\right)$, J. Fac. Sci. Tokyo Sect. IA 27 (1980), 157-179. Zbl0433.42019
- [10] M. Plancherel et G. Pólya, Fonctions entières intégrales de Fourier multiples, Comment. Math. Helv. 9 (1937), 224-248. Zbl63.0377.02
- [11] F. Ricci and E. M. Stein, Harmonic analysis on nilpotent groups and singular integrals II. Singular kernels supported on submanifolds, J. Funct. Anal. 78 (1988), 56-84. Zbl0645.42019
- [12] M. H. Taibleson and G. Weiss, The molecular characterization of certain Hardy spaces, Astérisque 77 (1980), 68-149. Zbl0472.46041

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