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Multiplication properties of the spacesB p,q s andF p,q s quasi-banach algebras of functions

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Summary

Let A be either B p, qs or F p, qs , where - ∞<s <∞; 0<p, q≦∞ (spaces of Besov-Hardy-Sobolev type, defined on Rn). (i) If g ∈C ϱ (Hölder-Zygmund spaces), then f → gf is a bounded operator from A into A, provided that ϱ=ϱ(s, p, q, n) is large enough. (ii) There are given sufficient conditions for s, p, and q ensuring that A is a subalgebra of C (space of uniformly continuous bounded functions on Rn).

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Entrata in Redazione il 17 marzo 1976.

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Triebel, H. Multiplication properties of the spacesB p,q s andF p,q s quasi-banach algebras of functions. Annali di Matematica 113, 33–42 (1977) doi:10.1007/BF02418365

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Keywords

  • Multiplication Property
  • Bounded Operator
  • Bounded Function
  • Continuous Bounded Function