Characterizations of variable exponent Hardy spaces via Riesz transforms

By Dachun Yang, Ciqiang Zhuo, E. Nakai. 2015

74 citations recorded by the source corpus.

Let $$p(\cdot ):\ \mathbb R^n\rightarrow (0,\infty )$$p(·):Rn→(0,∞) be a variable exponent function satisfying that there exists a constant $$p_0\in (0,p_-)$$p0∈(0,p-), where $$p_-:=\hbox {ess inf}_{x\in \mathbb R^n}p(x)$$p-:=essinfx∈Rnp(x), such that the Hardy–Littlewood maximal operator is bounded on the variable exponent Lebesgue space $$L^{p(\cdot )/p_0}(\mathbb R^n)$$Lp(·)/p0(Rn). In this article, via investigating relations between boundary values of harmonic functions on the upper half space and elements of variable exponent Hardy spaces $$H^{p(\cdot )}(\mathbb R^n)$$Hp(·)(Rn) introduced by E. Nakai and Y. Sawano and, independently, by D. Cruz-Uribe and L.-A. D. Wang, the authors characterize $$H^{p(\cdot )}(\mathbb R^n)$$Hp(·)(Rn) via the first order Riesz transforms when $$p_-\in (\frac{n-1}{n},\infty )$$p-∈(n-1n,∞), and via compositions of all the first order Riesz transforms when $$p_-\in (0,\frac{n-1}{n})$$p-∈(0,n-1n).

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/059c150f5b8c9dc1e2de909ac107d86f1c535970

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In Applied Mathematics

1. Dachun Yang
2. Wen Yuan
3. Jun Liu
4. Yangyang Zhang
5. Songbai Wang
6. Ferenc Weisz
7. Yoshihiro Sawano
8. Long Huang

In Mathematical Physics

1. Dachun Yang
2. Wen Yuan
3. Jun Liu
4. Yangyang Zhang
5. Songbai Wang
6. Ferenc Weisz
7. Yoshihiro Sawano
8. Ciqiang Zhuo

Citations in the corpus

• Variable Hardy–Lorentz spaces Hp(·),q(Rn) (2018, unknown): “[54] investigated Hp(⋅)(Rn) via Riesz transforms.”
• Variable Anisotropic Hardy Spaces and Their Applications (2017, background): “[81] further completed the theory of this space.”
• Weak Hardy-Type Spaces Associated with Ball Quasi-Banach Function Spaces II: Littlewood–Paley Characterizations and Real Interpolation (2019, background): “In recent decades, various variants of classical Hardy spaces have been introduced and their real-variable theories have been well developed; these variants include weighted Hardy spaces (see [68]), (weighted) Herz–Hardy spaces (see, for instance, [18, 30, 31, 56, 57]), (weighted) Hardy–Morrey space”
• Anisotropic Variable Hardy-Lorentz Spaces and Their Real Interpolation (2017, background): “[81] further completed the theory of these variable Hardy spaces.”