| Summary: | 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.
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