Bilinear Hilbert transforms and (sub)bilinear maximal functions along convex curves

where $p$ , $q$ , and $r$ satisfy $1 ∕ p + 1 ∕ q = 1 ∕ r$ , and $r > \frac{1}{2}$ , $p > 1$ , and $q > 1$ . Moreover, the same $L^{p} (ℝ) \times L^{q} (ℝ) \to L^{r} (ℝ)$ boundedness property holds for the corresponding (sub)bilinear maximal function $M_{γ} (f, g)$ along a convex curve $γ$

M_{γ} (f, g) (x) : = sup_{𝜀 > 0} \frac{1}{2 𝜀} \int_{- 𝜀}^{𝜀} | f (x - t) g (x - γ (t)) | d t .

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Keywords

bilinear Hilbert transform, (sub)bilinear maximal function, convex curve, time frequency analysis

Mathematical Subject Classification

Primary: 42B20

Secondary: 47B38

Milestones

Received: 7 June 2020

Revised: 2 September 2020

Accepted: 4 September 2020

Published: 8 March 2021

Authors

Junfeng Li
School of Mathematical Sciences Dalian University of Technology Dalian China

Haixia Yu
Department of Mathematics Shantou University Shantou China

Vol. 310, No. 2, 2021

Junfeng Li and Haixia Yu

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification

Milestones

Authors