Pseudo-differential operators of infinite order on $$W^{\Omega }_{M}(\mathbb C^{n})$$ W M Ω ( C n ) -space involving fractional Fourier transform

Abstract

The mapping properties of pseudo-differential operators associated with symbol θ(z, ξ), z = x + iy and ξ = u + it on W M (C n )-space are investigated. Motivated from Wong (An introduction to pseudo-differential operators. World Scientific, Singapore, 2014), L p (R n )-boundedness of pseudo-differential operators on W M (C n )-space is studied by using the fractional Fourier transform.