Pseudo-differential calculi and entropy estimates with Orlicz modulation spaces

Gumber A., Rana N., Toft J., ÜSTER R.

Journal of Functional Analysis, cilt.286, sa.3, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 286 Sayı: 3
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1016/j.jfa.2023.110225
  • Dergi Adı: Journal of Functional Analysis
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Anahtar Kelimeler: Entropy functional, Essential inverse, Orlicz modulation spaces, Pseudo-differential operator
  • İstanbul Üniversitesi Adresli: Evet

Özet

We deduce continuity properties for pseudo-differential operators with symbols in Orlicz modulation spaces when acting on other Orlicz modulation spaces. In particular we extend well-known results in the literature. For example we generalize the classical result by Cordero and Nicola that if [Formula presented], pj,qj⩽q′,q⩽p and a∈Mp,q, then the pseudo-differential operator Op(a) is continuous from Mp1,q1 to Mp2′,q2′. We also show that the entropy functional Eϕ possess suitable continuity properties on a suitable Orlicz modulation space MΦ satisfying Mp⊆MΦ⊆M2, though Eϕ is discontinuous on M2=L2.