Hörmander multiplier theorem with regularity in modulation spaces

2020 ◽  
Vol 197 ◽  
pp. 111789
Author(s):  
Liang Huang ◽  
Chengdan Xu
Keyword(s):  
Modulation Spaces ◽  
Multiplier Theorem

Applications of Erdélyi-Kober fractional integral for solving time-fractional Tricomi-Keldysh type equation

2020 ◽  
Vol 23 (5) ◽  
pp. 1381-1400 ◽  
Author(s):  
Kangqun Zhang
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Integral Operator ◽  
Nonlinear Equations ◽  
Existence And Uniqueness ◽  
Fractional Integral ◽  
Formal Solution ◽  
Type Equation ◽  
Multiplier Theorem ◽  
Problem Of Time

Abstract In this paper we consider Cauchy problem of time-fractional Tricomi-Keldysh type equation. Based on the theory of a Erdélyi-Kober fractional integral operator, the formal solution of the inhomogeneous differential equation involving hyper-Bessel operator is presented with Mittag-Leffler function, then nonlinear equations are considered by applying Gronwall-type inequalities. At last, we establish the existence and uniqueness of L p -solution of time-fractional Tricomi-Keldysh type equation by use of Mikhlin multiplier theorem.

scholarly journals Schatten p-class property of pseudodifferential operators with symbols in modulation spaces

2012 ◽  
Vol 205 ◽  
pp. 119-148
Author(s):  
Masaharu Kobayashi ◽  
Akihiko Miyachi
Keyword(s):  
Pseudodifferential Operators ◽  
Modulation Spaces

AbstractIt is proved that the pseudodifferential operators σt(X, D) belong to the Schatten p-class Cp, 0 < p ≤ 2, if the symbol σ(x,ω) is in certain modulation spaces on

Non-integer power estimate in modulation spaces and its applications

2017 ◽  
Vol 60 (8) ◽  
pp. 1443-1460 ◽  
Author(s):  
JieCheng Chen ◽  
Qiang Huang ◽  
XiangRong Zhu
Keyword(s):  
Modulation Spaces ◽  
Power Estimate ◽  
Integer Power
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