The atomic decomposition of Besov-Bergman-Lipschitz spaces

Author:
Geraldo Soares De Souza

Journal:
Proc. Amer. Math. Soc. **94** (1985), 682-686

MSC:
Primary 46E35; Secondary 42C15

DOI:
https://doi.org/10.1090/S0002-9939-1985-0792283-5

MathSciNet review:
792283

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Abstract | References | Similar Articles | Additional Information

Abstract: Let denote a special atom, or, for any interval is the left half of , is the right half, denotes the length of and the characteristic function of . For , let be special atoms and a sequence of real numbers; then we define the space

In the early 1960s, the following spaces were introduced, now known as Besov-Bergman-Lipschitz spaces. For , , , let

Now we write down the main theorem of this paper which is as follows.

THEOREM for if and only if . Moreover, there are absolute constants and such that

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1985-0792283-5

Keywords:
Besov-Bergman-Lipschitz spaces,
equivalence of Banach spaces,
analytic functions,
atomic decomposition

Article copyright:
© Copyright 1985
American Mathematical Society