Martingale Morrey-Campanato Spaces and Fractional Integrals

By E. Nakai, Gaku Sadasue. 2012

67 citations recorded by the source corpus.

We introduce Morrey-Campanato spaces of martingales and give their basic properties. Our definition of martingale Morrey-Campanato spaces is different from martingale Lipschitz spaces introduced by Weisz, while Campanato spaces contain Lipschitz spaces as special cases. We also give the relation between these definitions. Moreover, we establish the boundedness of fractional integrals as martingale transforms on these spaces. To do this we show the boundedness of the maximal function on martingale Morrey-Campanato spaces.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/b383bbefd1d8d488cab7e777761a5b01d8ca08d9

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In Applied Mathematics

1. Yong Jiao
2. Lian Wu
3. Yoshihiro Sawano
4. Dachun Yang
5. Wen Yuan
6. Ciqiang Zhuo
7. Shohei Nakamura
8. Kwok-Pun Ho

Citations in the corpus

• A Thought on Generalized Morrey Spaces (2018, background): “,r>0 ϕ(x,r) 1 |Q(x,r)| Z Q(x,r) |f(y)|qdy !1 q <∞. (5.6) See [4, 30, 46, 76] for the approach to this direction. 5.5 Martingale Morrey spaces One can use martingales to generalize Morrey spaces [80, 84]. Let (Ω,Σ,P) be a probability space, and F = {Fn}n≥0 a nondecreasing sequence of sub-σ-alge”
• The predual and John-Nirenberg inequalities on generalized BMO martingale spaces (2014, background): “Recently, Nakai and Sadasue [17] extended the notion of fractional integrals to more general martingales.”