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Hörmander Type Multipliers on Anisotropic Hardy Spaces.
- Source :
- Acta Mathematica Sinica; Nov2019, Vol. 35 Issue 11, p1841-1853, 13p
- Publication Year :
- 2019
-
Abstract
- The main purpose of this paper is to establish, using the Littlewood-Paley-Stein theory (in particular, the Littlewood-Paley-Stein square functions), a Calderón-Torchinsky type theorem for the following Fourier multipliers on anisotropic Hardy spaces H<superscript>p</superscript> (ℝ<superscript>n</superscript>; A) associated with expensive dilation A: T m f (x) = ∫ ℝ n m (ξ) f ^ (ξ) e 2 π i x ⋅ ξ d ξ . Our main Theorem is the following: Assume that m(ξ) is a function on ℝ<superscript>n</superscript> satisfying sup j ∈ ℤ ‖ m j ‖ W s (A ∗) < ∞ with s > ζ − − 1 (1 p − 1 2) Then T<subscript>m</subscript> is bounded from H<superscript>p</superscript>(ℝ<superscript>n</superscript>; A) to H<superscript>p</superscript>(ℝ<superscript>n</superscript>; A) for all 0 < p ≤ 1 and ‖ T m ‖ H A p → H A p ≲ sup j ∈ ℤ ‖ m j ‖ W s (A ∗) , where A* denotes the transpose of A. Here we haveusedthe notations m<subscript>j</subscript> (ξ)= m(A*<superscript>j</superscript>ξ)φ(ξ)and is a suitable cut-off function on ℝ<superscript>n</superscript>, and W<superscript>s</superscript>(A*) is an anisotropic Sobolev space associated with expansive dilation A* on ℝ<superscript>n</superscript>. [ABSTRACT FROM AUTHOR]
- Subjects :
- HARDY spaces
MULTIPLIERS (Mathematical analysis)
SOBOLEV spaces
Subjects
Details
- Language :
- English
- ISSN :
- 14398516
- Volume :
- 35
- Issue :
- 11
- Database :
- Complementary Index
- Journal :
- Acta Mathematica Sinica
- Publication Type :
- Academic Journal
- Accession number :
- 139163044
- Full Text :
- https://doi.org/10.1007/s10114-019-8071-8