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Martingale Morrey-Campanato spaces and fractional integrals. (English) Zbl 1254.46035
Summary: 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.
46E30Spaces of measurable functions
42B25Maximal functions, Littlewood-Paley theory
60G46Martingales and classical analysis