On the quotient quantum graph with respect to the regular representation
Topological Equivalence of nonautonomous difference equations with a family of dichotomies on the half line
Dual spaces of mixed-norm martingale hardy spaces
Ferenc Weisz
Department of Numerical Analysis, Eötvös L. University, H-1117 Budapest, Pázmány P. sétány 1/C., Hungary
Fund Project: This research was supported by the Hungarian National Research, Development and Innovation Office-NKFIH, KH130426
In this paper, we generalize the Doob's maximal inequality for mixed-norm $ L_{\vec{p}} $ spaces. We consider martingale Hardy spaces defined with the help of mixed $ L_{{\vec{p}}} $-norm. A new atomic decomposition is given for these spaces via simple atoms. The dual spaces of the mixed-norm martingale Hardy spaces is given as the mixed-norm $ BMO_{\vec{r}}(\vec{\alpha}) $ spaces. This implies the John-Nirenberg inequality $ BMO_{1}(\vec{\alpha}) \sim BMO_{\vec{r}}(\vec{\alpha}) $ for $ 1<\vec{r}<\infty $. These results generalize the well known classical results for constant $ p $ and $ r $.
Keywords: Mixed Lebesgue spaces, mixed martingale Hardy spaces, atomic decompositions, Doob's inequality, $ BMO $ spaces, John-Nirenberg inequality.
Mathematics Subject Classification: Primary: 42B35; Secondary: 42B30, 60G42, 42B25, 46E30.
Citation: Ferenc Weisz. Dual spaces of mixed-norm martingale hardy spaces. Communications on Pure & Applied Analysis, doi: 10.3934/cpaa.2020285
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