Bilinear Operators on Homogeneous Groups
نویسندگان
چکیده
Let Hp denote the Lebesgue space Lp for p > 1 and the Hardy space Hp for p ≤ 1. For 0 < p, q, r < ∞, we study Hp × Hq → Hr mapping properties of bilinear operators given by finite sums of products of Calderón–Zygmund operators on stratified homogeneous Lie groups. When r ≤ 1, we show that such mapping properties hold when a number of moments of the operator vanish. This hypothesis is natural and the conditions imposed are the minimal required for any operator of this type to map into the space Hr. Our proofs employ both the maximal function and atomic characterization of Hp. We also discuss some applications.
منابع مشابه
Cohomology of aff(1|1) acting on the space of bilinear differential operators on the superspace IR1|1
We consider the aff(1)-module structure on the spaces of bilinear differential operators acting on the spaces of weighted densities. We compute the first differential cohomology of the Lie superalgebra aff(1) with coefficients in space Dλ,ν;µ of bilinear differential operators acting on weighted densities. We study also the super analogue of this problem getting the same results.
متن کاملBilinear Fourier Integral Operators
We study the boundedness of bilinear Fourier integral operators on products of Lebesgue spaces. These operators are obtained from the class of bilinear pseudodifferential operators of Coifman and Meyer via the introduction of an oscillatory factor containing a real-valued phase of five variables Φ(x, y1, y2, ξ1, ξ2) which is jointly homogeneous in the phase variables (ξ1, ξ2). For symbols of or...
متن کاملH ¨ Older Type Inequalities for Orthosymmetric Bilinear Operators 1
The homogeneous functional calculus on vector lattices is a useful tool in a variety of areas. One of the interesting application is the study of powers of Banach lattices initiated by G. Ya. Lozanovskĭı [18]. Recently G. Buskes and A. van Rooij [8] introduced the concept of squares of Archimedean vector lattices which allows to represent orthoregular bilinear operators as linear regular operat...
متن کاملL-FUZZY BILINEAR OPERATOR AND ITS CONTINUITY
The purpose of this paper is to introduce the concept of L-fuzzybilinear operators. We obtain a decomposition theorem for L-fuzzy bilinearoperators and then prove that a L-fuzzy bilinear operator is the same as apowerset operator for the variable-basis introduced by S.E.Rodabaugh (1991).Finally we discuss the continuity of L-fuzzy bilinear operators.
متن کاملBilinear Operators on Herz-type Hardy Spaces
The authors prove that bilinear operators given by finite sums of products of Calderón-Zygmund operators on Rn are bounded from HK̇11 q1 × HK̇ α2,p2 q2 into HK̇ q if and only if they have vanishing moments up to a certain order dictated by the target space. Here HK̇ q are homogeneous Herz-type Hardy spaces with 1/p = 1/p1 +1/p2, 0 < pi ≤ ∞, 1/q = 1/q1 +1/q2, 1 < q1, q2 < ∞, 1 ≤ q < ∞, α = α1 + α2 a...
متن کامل