TY - JOUR
T1 - Pseudo differential Operators on Mixed-Norm α-Modulation Spaces
AU - Nielsen, Morten
N1 - Publisher Copyright:
© Rocky Mountain Mathematics Consortium.
PY - 2023/6
Y1 - 2023/6
N2 - Mixed-norm α-modulation spaces were introduced recently by Cleanthous and Georgiadis (Trans. Amer. Math. Soc. 373:5 (2020), 3323–3356). The mixed-norm α-modulation spaces (Formular Presented), form a family of smoothness spaces that contains the mixed-norm Besov spaces as special cases. We prove that a pseudodifferential operator σ(x, D) with symbol in the Hörmander class (Formular Presented) extends to a bounded operator (Formular Presented), provided (Formular Presented), and 0 (Formular Presented). This extends the known result that pseudodifferential operators, with symbol in the class S1b, maps the mixed-norm Besov space (Formular Presented).
AB - Mixed-norm α-modulation spaces were introduced recently by Cleanthous and Georgiadis (Trans. Amer. Math. Soc. 373:5 (2020), 3323–3356). The mixed-norm α-modulation spaces (Formular Presented), form a family of smoothness spaces that contains the mixed-norm Besov spaces as special cases. We prove that a pseudodifferential operator σ(x, D) with symbol in the Hörmander class (Formular Presented) extends to a bounded operator (Formular Presented), provided (Formular Presented), and 0 (Formular Presented). This extends the known result that pseudodifferential operators, with symbol in the class S1b, maps the mixed-norm Besov space (Formular Presented).
KW - Besov space
KW - hypoelliptic operator
KW - modulation space
KW - pseudodifferential operator
KW - α-modulation space
UR - http://www.scopus.com/inward/record.url?scp=85167973269&partnerID=8YFLogxK
U2 - 10.1216/rmj.2023.53.875
DO - 10.1216/rmj.2023.53.875
M3 - Journal article
AN - SCOPUS:85167973269
SN - 0035-7596
VL - 53
SP - 875
EP - 887
JO - Rocky Mountain Journal of Mathematics
JF - Rocky Mountain Journal of Mathematics
IS - 3
ER -