Linear and bilinear Fourier multipliers on Orlicz modulation spaces

Blasco O., Öztop S., Üster R.

Monatshefte fur Mathematik, cilt.204, sa.4, ss.679-705, 2024 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 204 Sayı: 4
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1007/s00605-023-01937-9
  • Dergi Adı: Monatshefte fur Mathematik
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Sayfa Sayıları: ss.679-705
  • Anahtar Kelimeler: 42B15, 42B35, 46E30, Bilinear multipliers, Fourier multiplier, Orlicz modulation spaces, Primary 42A45, Weighted Orlicz spaces
  • İstanbul Üniversitesi Adresli: Evet

Özet

Let Φ i, Ψ i be Young functions, ωi be weights and MωiΦi,Ψi(Rd) be the corresponding Orlicz modulation spaces for i= 1 , 2 , 3 . We consider linear (respect. bilinear) multipliers on Rd , that is bounded measurable functions m(ξ) (respect. m(ξ, η)) on Rd (respect. R2d) such that Tm(f)(x)=∫Rdf^(ξ)m(ξ)e2πi⟨ξ,x⟩dξ (respect. Bm(f1,f2)(x)=∫Rd∫Rdf1^(ξ)f2^(η)m(ξ,η)e2πi⟨ξ+η,x⟩dξdη define a bounded linear (respect. bilinear) operator from Mω1Φ1,Ψ1(Rd) to Mω2Φ2,Ψ2(Rd) (respect. Mω1Φ1,Ψ1(Rd)×Mω2Φ2,Ψ2(Rd) to Mω3Φ3,Ψ3(Rd)). In this paper we study some properties of these spaces and give methods to generate linear and bilinear multipliers between Orlicz modulation spaces.