Liouville's theorem for first-order partial differential operators

In this paper, we shall estimate the growth order of the n-th derivative Cauchy integrals at a point in terms of the distance between the point and the boundary of the domain. By using the estimate, we shall generalize Plemelj-Sokthoski theorem. We also consider the boundary behavior of generalized Cauchy integrals on compact bordered Riemann surfaces.

On exceptional values of holomorphic mappings of Riemann surfaces

Alois Klíč (1980)

Časopis pro pěstování matematiky

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On the existence and uniqueness of solutions for an incomplete second-order abstract Cauchy problem

F. Periago, B. Straub (2003)

Studia Mathematica

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We prove existence and uniqueness of classical solutions for an incomplete second-order abstract Cauchy problem associated with operators which have polynomially bounded resolvent. Some examples of differential operators to which our abstract result applies are also included.

Norm inequalities for integral operators on cones

Yoram Sagher, M. Vali Siadat, Kecheng Zhou (1990)

Colloquium Mathematicae

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