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1
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p-Envelopes of non-locally convex F-spaces

100%
Eoff C.
Annales Polonici Mathematici
|
1992
|
tom 57
|
nr 2
121-134
EN
The p-envelope of an F-space is the p-convex analogue of the Fréchet envelope. We show that if an F-space is locally bounded (i.e., a quasi-Banach space) with separating dual, then the p-envelope coincides with the Banach envelope only if the space is already locally convex. By contrast, we give examples of F-spaces with are not locally bounded nor locally convex for which the p-envelope and the Fréchet envelope are the same.
2
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A characterization of completely bounded multipliers of Fourier algebras

100%
Jolissaint P.
Colloquium Mathematicum
|
1992
|
tom 63
|
nr 2
311-313
3
Content available remote

Pointwise multipliers on weighted BMO spaces

100%
Nakai E.
Studia Mathematica
|
1997
|
tom 125
|
nr 1
35-56
EN
Let E and F be spaces of real- or complex-valued functions defined on a set X. A real- or complex-valued function g defined on X is called a pointwise multiplier from E to F if the pointwise product fg belongs to F for each f ∈ E. We denote by PWM(E,F) the set of all pointwise multipliers from E to F. Let X be a space of homogeneous type in the sense of Coifman-Weiss. For 1 ≤ p < ∞ and for $ϕ: X×ℝ_{+} → ℝ_{+}$, we denote by $bmo_{ϕ,p}(X)$ the set of all functions $f ∈ L^{p}_{loc}(X)$ such that $sup_{a ∈ X, r>0} 1/ϕ(a,r) (1/μ(B(a,r)) ʃ_{B(a,r)} |f(x) -f_{B(a,r)}|^p dμ)^{1/p} < ∞$, where B(a,r) is the ball centered at a and of radius r, and $f_{B(a,r)}$ is the integral mean of f on B(a,r). Let $bmo_{ϕ}(X) = bmo_{ϕ,1}(X)$ and $bmo(X) = bmo_{1,1}(X)$. In this paper, we characterize $PWM(bmo_{ϕ1,p_1}(X), bmo_{ϕ2,p_2}(X))$. The following are examples of our results. $PWM(bmo_{(log(1/r))^{-α}}(𝕋^n),bmo_{(log(1/r))^{-β}}(𝕋^n)) = bmo_{(log(1/r))^{α-β-1}}(𝕋^n)$, 0≤β < α < 1, $PWM (bmo_{(log(1/r))^{-1}}(𝕋^n),bmo(𝕋^n)) = bmo_{(log log(1/r))^{-1}}(𝕋^n),$ $PWM (bmo(ℝ^n),bmo_{log(|a|+r+1/r),p}(ℝ^n)) = bmo(ℝ^n)$, 1 < p < ∞, etc.
4
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Pseudo-MV algebra of fractions and maximal pseudo-MV algebra of quotients

75%
Piciu D.
Open Mathematics
|
2004
|
tom 2
|
nr 2
199-217
EN
The aim of this paper is to define the notions of pseudo-MV algebra of fractions and maximal pseudo-MV algebra of quotients for a pseudo-MV algebra (taking as a guide-line the elegant construction of complete ring of quotients by partial morphisms introduced by G. Findlay and J. Lambek-see [14], p.36). For some informal explanations of the notion of fraction see [14], p. 37. In the last part of this paper the existence of the maximal pseudo-MV algebra of quotients for a pseudo-MV algebra (Theorem 4.5) is proven and I give explicit descriptions of this MV-algebra for some classes of pseudo MV-algebras.
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