Article ID: MTJPAM-D-23-00009

Title: Multilinear multipliers of function spaces with wavelet transform in Lorentz spaces

Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-23-00009; Volume 6 / Issue 3 / Year 2024, Pages 34-47

Document Type: Research Paper

Author(s): ‪İrem Adıyaman a , Öznur Kulak b

aDepartment of Mathematics, Institute of Sciences, Amasya University, Amasya, Turkey

bDepartment of Mathematics, Faculty of Arts and Sciences, Amasya University, Amasya, Turkey

Received: 26 May 2023, Accepted: 7 October 2023, Published: 25 October 2023

Corresponding Author: Öznur Kulak (Email address:

Full Text: PDF


Let 1 ≤ pi, qi, ri < ∞, si ∈ ℝ+  (i = 1, …, d + 1) and wi, vi (i = 1, …, d + 1) be weight functions on . Let Lsi(W)wi, vipi,qi, ri(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 d is said to be a multilinear multiplier on of type L(W)(pi, qi, ri,wi, vi, si), if the multilinear operator Bm associated with the m

    B_{m}(f_{1},\dots,f_{d})(x)=\underset{\mathbb{R}^{d}}{\int }\widehat{f_{1}}(\xi _{1})\dots\widehat{f_{d}}(\xi _{d})m(\xi_{1},\dots,\xi_{d})e^{2\pi i\left\langle \xi_{1}+\cdots+\xi_{d},x\right\rangle}d\xi_{1}\dots d\xi_{d}

defines a bounded multilinear operator from

    L_{s_{1}}(W)_{w_{1},v_{1}}^{p_{1},q_{1},r_{1}}(\mathbb{R})\times \dots\times L_{s_{d}}(W)_{w_{d},v_{d}}^{p_{d},q_{d},r_{d}}(\mathbb{R})\text{\ \ into \  }L_{s_{d+1}}(W)_{w_{d+1},v_{d+1}}^{p_{d+1},q_{d+1},r_{d+1}}(\mathbb{R}).

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.

Keywords: Multilinear multiplier, Lorentz space, wavelet transform

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