New real-variable characterizations of Musielak-Orlicz Hardy spaces

By Yiyu Liang, Jizheng Huang, Dachun Yang. 2012

81 citations recorded by the source corpus.

Abstract Let φ : R n × [ 0 , ∞ ) → [ 0 , ∞ ) be such that φ ( x , ⋅ ) is an Orlicz function and φ ( ⋅ , t ) is a Muckenhoupt A ∞ ( R n ) weight. The Musielak–Orlicz Hardy space H φ ( R n ) is defined to be the space of all f ∈ S ′ ( R n ) such that the grand maximal function f ∗ belongs to the Musielak–Orlicz space L φ ( R n ) . Luong Dang Ky established its atomic characterization. In this paper, the authors establish some new real-variable characterizations of H φ ( R n ) in terms of the vertical or the non-tangential maximal functions, or the Littlewood–Paley g -function or g λ ∗ -function, via first establishing a Musielak–Orlicz Fefferman–Stein vector-valued inequality. Moreover, the range of λ in the g λ ∗ -function characterization of H φ ( R n ) coincides with the known best results, when H φ ( R n ) is the classical Hardy space H p ( R n ) , with p ∈ ( 0 , 1 ] , or its weighted variant.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b7129fff921fc5caea973b87ff5d23ec97b45107

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In Applied Mathematics

1. Dachun Yang
2. Ciqiang Zhuo
3. Yiyu Liang
4. Luong Dang Ky
5. Wen Yuan
6. Sibei Yang
7. Jun Liu
8. Yoshihiro Sawano

In Mathematical Physics

1. Dachun Yang
2. Ciqiang Zhuo
3. Yiyu Liang
4. Luong Dang Ky
5. Wen Yuan
6. Yoshihiro Sawano
7. Sibei Yang
8. Jun Liu

Citations in the corpus

• FUNCTION SPACES WITH VARIABLE EXPONENTS – AN INTRODUCTION – (2014, unknown): “See also [12, 15, 109, 111, 228] for Musielak-Orlicz-Hardy spaces.”
• Intrinsic Square Function Characterizations of Hardy Spaces with Variable Exponents (2014, background): “[26] established the Littlewood-Paley g-function and the g∗ λ-function characterizations of H (R).”
• New Hardy Spaces of Musielak–Orlicz Type and Boundedness of Sublinear Operators (2011, background): “Recently, new Hardy spaces of Musielak–Orlicz type have developed in many directions (see [11,47,50,56,57]), some their characterizations and applications were also established and studied in [11,27,38,50].”
• Musielak-Orlicz Campanato Spaces and Applications (2013, background): “Observe that i(φ) may not be attainable, namely, φ may not be of uniformly lower type i(φ) (see [26]).”