The Convergence of Calderón Reproducing Formulae of Two Parameters on Some Classical Function Spaces

Kun-chuan Wang

Department of Applied Mathematics

National Dong Hwa University

kcwang@gms.ndhu.edu.tw

The Calderón reproducing formula is the most important in the study of harmonic analysis, which has the same property as the one of approximate identity in many special function spaces. In this talk, we use the idea of separation variables and molecular decomposition to extend single parameter into two-parameters and discuss the convergence of Calderón reproducing formula of two-parameters in some generalized function spaces of two parameters. Mainly, we focus on Besov spaces in two-parameter and show that these spaces are well-defined by Plancherel-Pôlya inequalities. Consequently, we obtain the norm equivalence between Besov spaces and corresponding sequence space in two-parameter. Also we show the convergence of Calderón reproducing formula in Besov space.

Keyword: atomic decomposition, Calderón reproducing formula, Littlewood-Paley, Plancherel-Pôlya inequality

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