Variable Anisotropic Hardy Spaces and Their Applications

By Jun Liu, Ferenc Weisz, Dachun Yang, Wen Yuan. Taiwanese journal of mathematics, 2017

56 citations recorded by the source corpus.

Let p(·) : R → (0,∞] be a variable exponent function satisfying the globally log-Hölder continuous condition and A a general expansive matrix on R. In this article, the authors first introduce the variable anisotropic Hardy space H p(·) A (R) associated with A, via the non-tangential grand maximal function, and then establish its radial or non-tangential maximal function characterizations. Moreover, the authors also obtain various equivalent characterizations of H p(·) A (R), respectively, by means of atoms, finite atoms, the Lusin area function, the Littlewood-Paley g-function or g∗ λ-function. As applications, the authors first establish a criterion on the boundedness of sublinear operators from H p(·) A (R) into a quasi-Banach space. Then, applying this criterion, the authors show that the maximal operators of the Bochner-Riesz and the Weierstrass means are bounded from H p(·) A (R) to Lp(·)(Rn) and, as consequences, some almost everywhere and norm convergences of these Bochner-Riesz and Weierstrass means are also obtained. These results on the Bochner-Riesz and the Weierstrass means are new even in the isotropic case.

Subfields: Applied Mathematics, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/bcfef87f6e040171ba8fb65f628449f383522d20

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

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

In Mathematical Physics

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

In Statistics and Probability

1. Wen Yuan
2. Dachun Yang
3. Jun Liu

Citations in the corpus

• Atomic and Littlewood–Paley Characterizations of Anisotropic Mixed-Norm Hardy Spaces and Their Applications (2018, methodology): “For more progresses about the theory of anisotropic function spaces on R, we refer the reader to [11, 25, 45, 48, 49, 51, 53, 54, 55] for anisotropic Hardy-type spaces and to [7, 8, 9, 46, 47, 56] for anisotropic Besov and TriebelLizorkin spaces.”