Multilinear multipliers of function spaces with wavelet transform in lorentz spaces

Abstract

Let 1 ≤ pi, qi, ri < ∞, si ∈ℝ+ (i = 1,..., d + 1) and wi, vi (i = 1,..., d + 1) be weight functions on ℝ. Let Lsi (W)pi , qi , ri/wi , vi (ℝ) (i = 1,..., d + 1) be weighted normed spaces of functions whose wavelet transforms are in Lorentz space. A bounded function m(ξ1,..., ξd) defined on ℝd is said to be a multilinear multiplier on ℝ of type L(W)(pi, qi, ri,wi, vi, si), if the multilinear operator Bm associated with the m defines a bounded multilinear operator from Also BM[L(W)(pi, qi, ri,wi, vi, si)] denotes the space of all multilinear multipliers of type L(W)(pi, qi, ri,wi, vi, si). In this work, we discuss the behaviour of the multilinear multipliers under the translation and modulation operators. Moreover, we give methods of construction examples of multilinear multipliers. © 2024, MTJPAM Turkey. All rights reserved.