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Full-Text Articles in Physical Sciences and Mathematics
Good Stein Neighborhood Bases For Nonsmooth Pseudoconvex Domains, Chizuko Iwaki
Good Stein Neighborhood Bases For Nonsmooth Pseudoconvex Domains, Chizuko Iwaki
Graduate Theses and Dissertations
In 1979, Dufresnoy showed that the existence of a good Stein neighborhood base for Ω ⊂ℂⁿ implies that one can solve the inhomogeneous Cauchy-Riemann equations in C^∞(Ω̄), even if the boundary of Ω is only Lipschitz. In my thesis, I will show sufficient conditions for the existence of a good Stein neighborhood base on a Lipschitz domain satisfying Property (P).
Isometries Of Besov Type Spaces Among Composition Operators, Melissa Ann Shabazz
Isometries Of Besov Type Spaces Among Composition Operators, Melissa Ann Shabazz
Graduate Theses and Dissertations
Let Bp,alpha for p >1 and alpha >1 be the Besov type space of holomorphic functions on the unit disk D. Given Phi, a holomorphic self map of D, we show the composition operator CPhi is an isometry on Bp,alpha if and only if the weighted composition operator WPhiPhi, is an isometry on the weighted Bergman space Ap,alpha. We then characterize isometries among composition operators in Bp,alpha in terms of their Nevanlinna type counting function. Finally, we find that the only isometries among composition operators on Bp,alpha, except on B 2,0, are induced by rotations. This extends known results by …