Applications of Hardy Spaces Associated with Ball Quasi-Banach Function Spaces
By Fan Wang, Dachun Yang, Sibei Yang. Results in Mathematics, 2019
85 citations recorded by the source corpus.
Let X be a ball quasi-Banach function space satisfying some minor assumptions. In this article, the authors establish the characterizations of $$H_X(\mathbb {R}^n)$$ H X ( R n ) , the Hardy space associated with X , via the Littlewood–Paley g -functions and $$g_\lambda ^*$$ g λ ∗ -functions. Moreover, the authors obtain the boundedness of Calderón–Zygmund operators on $$H_X(\mathbb {R}^n)$$ H X ( R n ) . For the local Hardy-type space $$h_X(\mathbb {R}^n)$$ h X ( R n ) associated with X , the authors also obtain the boundedness of $$S^0_{1,0}(\mathbb {R}^n)$$ S 1 , 0 0 ( R n ) pseudo-differential operators on $$h_X(\mathbb {R}^n)$$ h X ( R n ) via first establishing the atomic characterization of $$h_X(\mathbb {R}^n)$$ h X ( R n ) . Furthermore, the characterizations of $$h_X(\mathbb {R}^n)$$ h X ( R n ) by means of local molecules and local Littlewood–Paley functions are also given. The results obtained in this article have a wide range of generality and can be applied to the classical Hardy space, the weighted Hardy space, the Herz–Hardy space, the Lorentz–Hardy space, the Morrey–Hardy space, the variable Hardy space, the Orlicz-slice Hardy space and their local versions. Some special cases of these applications are even new and, particularly, in the case of the variable Hardy space, the $$g_\lambda ^*$$ g λ ∗ -function characterization obtained in this article improves the known results via widening the range of $$\lambda $$ λ .
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/78c841fe9f9291b286d1e4014bc58f85b7bae266
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
Citations in the corpus
- Hardy spaces associated with ball quasi‐Banach function spaces on spaces of homogeneous type: Characterizations of maximal functions, decompositions, and dual spaces (2021, methodology): “[71] further established the Littlewood–Paley g-function and g λ -function characterizations of bothHX(R) and its localized version hX(R) and obtained the boundedness of both Calderón–Zygmund operators and pseudo-differential operators, respectively, on HX(R) and hX(R).”
- Intrinsic square function characterizations of Hardy spaces associated with ball quasi-Banach function spaces (2020, methodology): “[26] further established the characterizations of HX(R) and hX(R), respectively, in terms of the Littlewood–Paley g-functions and g∗ λ-functions, and obtained the boundedness of Calderón– Zygmund operators and pseudo-differential operators, respectively, on HX(R) and hX(R).”