An algebra containing the two-sided convolution operators
نویسندگان
چکیده
منابع مشابه
An Algebra Containing the Two-Sided Convolution Operators
We present an intrinsically defined algebra of operators containing the right and left invariant Calderón-Zygmund operators on a stratified group. The operators in our algebra are pseudolocal and bounded on Lp (1 < p <∞). This algebra provides an example of an algebra of singular integrals that falls outside of the classical Calderón-Zygmund theory.
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where ψ{v) = u, u. R. O'Neil obtained sharp upper and lower estimates when ψ(u) — u and n — 2, [3, Lemma 1.5]. Our results coincide with his for this case. We were able to apply our estimates for the case ψ(u) = u (^-arbitrary) to classical Fourier transform inequalities of Hardy and Little wood. The main problem of this paper is to determine whether or not one can obtain the same types of uppe...
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1. Let X be a Banach space, and B(X) the Banach algebra of all bounded linear operators in X. The closed two sided ideals of B(X) (actually, of any Banach algebra) form a complete lattice L(X). Aside from very concrete cases, L(X) has not yet been determined; for instance, when X = l, l ^ p < « > , L(X) is a chain (i.e., totally ordered) with three elements: {o}, B(X) and the ideal C(X) of comp...
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A general form of a family of bounded two-sided continuous distributions is introduced. The uniform and triangular distributions are possibly the simplest and best known members of this family. We also describe families of continuous distribution on a bounded interval generated by convolutions of these two sided distributions. Examples of various forms of convolutions of triangular distribution...
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Let G be a locally compact abelian group, let m be a bounded complex-valued Borel measure on G; and let Tm be the corresponding convolution operator on LðGÞ: Let X be a Banach space and let S be a continuous linear operator on X : Then we show that every linear operator F : X ! LðGÞ such that FS 1⁄4 TmF is continuous if and only if the pair ðS;TmÞ has no critical eigenvalue. # 2002 Elsevier Sci...
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2008
ISSN: 0001-8708
DOI: 10.1016/j.aim.2008.04.014