Unbounded holomorphic Fourier multipliers on starlike Lipschitz surfaces and applications to Sobolev spaces

By a generalization of Fueter’s result, we establish the correspondence between the convolution operators and the Fourier multipliers on starlike Lipschitz surfaces. As applications, we obtain the Sobolev-boundedness of the Fourier multipliers and prove the equivalence between two classes of Hardy–Sobolev spaces on starlike Lipschitz surfaces.