Abstract
Let D be a weakly q-convex domain in the complex projective space ℂPn. In this paper, the (weighted) ∂-Cauchy problem with support conditions in D is studied. Specifically, the modified weight function method is used to study the L2 existence theorem for the ∂-Neumann problem on D. The solutions are used to study function theory on weakly q-convex domains via the ∂-Cauchy problem.
Highlights
Introduction and PreliminariesAs mentioned in the abstract, the main aim of this note is to introduce the notion of an almost anti-periodic function in Banach space as well as to prove some characterizations for this class of functions
The main result of paper is Theorem 2.3, in which we completely profile the closure of linear span of almost anti-periodic functions in the space of almost periodic functions
We prove some other statements regarding almost anti-periodic functions, and introduce the concepts of Stepanov almost anti-periodic functions, asymptotically almost anti-periodic functions and Stepanov asymptotically almost anti-periodic functions
Summary
Introduction and PreliminariesAs mentioned in the abstract, the main aim of this note is to introduce the notion of an almost anti-periodic function in Banach space as well as to prove some characterizations for this class of functions. We introduce the notion of an almost anti-periodic function as follows. Consider the functions f1(t) = f2(t) = cos t, t ∈ R, which are clearly (almost) anti-periodic.
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