Projects per year
Abstract
Let (Formula presented.) be a metric measure space endowed with a distance (Formula presented.) and a nonnegative Borel doubling measure (Formula presented.). Let (Formula presented.) be a secondorder nonnegative selfadjoint operator on (Formula presented.). Assume that the semigroup (Formula presented.) generated by (Formula presented.) satisfies Gaussian upper bounds. In this article we establish a discrete characterization of weighted Hardy spaces (Formula presented.) associated with (Formula presented.) in terms of the area function characterization, and prove its weighted atomic decomposition, where (Formula presented.) and a weight (Formula presented.) is in the Muckenhoupt class (Formula presented.). Further, we introduce a Moser type estimate for (Formula presented.) to show the discrete characterization for the weighted Hardy spaces (Formula presented.) associated with (Formula presented.) in terms of the Littlewood–Paley function and obtain the equivalence between the weighted Hardy spaces in terms of the Littlewood–Paley function and area function.
Original language  English 

Pages (fromto)  16171646 
Number of pages  30 
Journal  Journal of Geometric Analysis 
Volume  26 
Issue number  2 
DOIs  
Publication status  Published  1 Apr 2016 
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Projects
 1 Finished

Harmonic analysis: Function spaces and singular integral operators
13/02/12 → 31/12/17
Project: Research