Strongly singular integrals along curves on α-modulation spaces

摘要

In this paper, we study the strongly singular integrals Tn,β,γf(x)=p.v.∫−11f(x−Γθ(t))e−2πi|t|−βt|t|γdt along homogeneous curves Γθ(t). We prove that Tn,β,γ is bounded on the α-modulation spaces, including the inhomogeneous Besov spaces and the classical modulation spaces.