Convergence of Calderon formula for two parameters

• Main Authors: Jiang-Wei Huang, 黃建偉
• Other Authors: Kun-Chuan Wang
• Format: Others
• Published: 2015
• Online Access: http://ndltd.ncl.edu.tw/handle/34498873778151570862

碩士 === 國立東華大學 === 應用數學系 === 103 === The Calderón reproducing formula is the most important in the study of harmonic analysis, which has the same the property as the one of approximate identity in many special function spaces. In this thesis, we use the idea of separation variables and atomic decomposition to extend single parameter into two-parameters and discuss the convergence of Calderón reproducing formula of two-parameters in Lp(Rn1 Rn2), in S(Rn1 Rn2) and in S ′(Rn1 Rn2). Finally, we define 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.