Fourier multipliers for Hardy spaces on graded Lie groups

2021/01/19 by Qing Hong, Hong, Qing, Guorong Hu +3
Mathematics · #Advanced Harmonic Analysis Research #Mathematical Analysis and Transform Methods #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.2101.07499

Abstract

In this paper, we investigate the H^p(G) → L^p(G), 0< p ≤ 1, boundedness of multiplier operators defined via group Fourier transform on a graded Lie group G, where H^p(G) is the Hardy space on G. Our main result extends those obtained in [Colloq. Math. 165 (2021), 1--30], where the L¹(G)→ L^1,∞(G) and L^p(G) → L^p(G), 1< p <∞, boundedness of such Fourier multiplier operators were proved.

Citations

• Hardy spaces with variable exponents and generalized Campanato spaces
• Estimates for translation invariant operators in Lp spaces
• Parabolic maximal functions associated with a distribution, II

Related

• Fourier multipliers on graded Lie groups
• Fourier multipliers for Triebel-Lizorkin spaces on graded Lie groups
• On the boundedness of multilinear Fourier multipliers on Hardy spaces
• Fourier multipliers for Triebel-Lizorkin spaces on compact Lie groups
• A note on Fourier multipliers on the product Hardy spaces