Abstract
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.
Highlights
The purpose of this paper is to introduce Morrey-Campanato spaces of martingales
We establish the boundedness of fractional integrals as martingale transforms on these spaces
The Lebesgue space Lp plays an important role in martingale theory as well as in harmonic analysis
Summary
The purpose of this paper is to introduce Morrey-Campanato spaces of martingales. The Lebesgue space Lp plays an important role in martingale theory as well as in harmonic analysis. We establish the boundedness of fractional integrals as martingale transforms on Morrey-Campanato spaces. We prove the boundedness of fractional integrals Iα as martingale transforms on Morrey-Campanato spaces. We always suppose that every σ-algebra Fn is generated by countable atoms, with denoting by A Fn the set of all atoms in Fn. We define the fractional integral Iα as a martingale transform by 1.3. Lp,λ and Lp,λ are not always trivial set {0} even if λ > 0 and λ > 1, respectively This property is different from classical Morrey-Campanato spaces on Rn. The martingale f fn n≥0 is said to be Lp,λ-bounded if fn ∈ Lp,λ n ≥ 0 and supn≥0 fn Lp,λ < ∞.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
