Fourier Series in Banach spaces and Maximal Regularity
نویسندگان
چکیده
We consider Fourier series of functions in L(0, 2π;X) where X is a Banach space. In particular, we show that the Fourier series of each function in L(0, 2π;X) converges unconditionally if and only if p = 2 and X is a Hilbert space. For operator-valued multipliers we present the Marcinkiewicz theorem and give applications to differential equations. In particular, we characterize maximal regularity (in a slightly different version than the usual one) by Rsectoriality. Applications to non-autonomous problems are indicated. Mathematics Subject Classification (2000). Primary 42B15; Secondary 34G10.
منابع مشابه
Arens regularity of bilinear forms and unital Banach module spaces
Assume that $A$, $B$ are Banach algebras and that $m:Atimes Brightarrow B$, $m^prime:Atimes Arightarrow B$ are bounded bilinear mappings. We study the relationships between Arens regularity of $m$, $m^prime$ and the Banach algebras $A$, $B$. For a Banach $A$-bimodule $B$, we show that $B$ factors with respect to $A$ if and only if $B^{**}$ is unital as an $A^{**}$-module. Le...
متن کاملArens Regularity and Weak Amenability of Certain Matrix Algebras
Motivated by an Arens regularity problem, we introduce the concepts of matrix Banach space and matrix Banach algebra. The notion of matrix normed space in the sense of Ruan is a special case of our matrix normed system. A matrix Banach algebra is a matrix Banach space with a completely contractive multiplication. We study the structure of matrix Banach spaces and matrix Banach algebras. Then we...
متن کاملArens regularity of bilinear maps and Banach modules actions
Let $X$, $Y$ and $Z$ be Banach spaces and $f:Xtimes Y longrightarrow Z$ a bounded bilinear map. In this paper we study the relation between Arens regularity of $f$ and the reflexivity of $Y$. We also give some conditions under which the Arens regularity of a Banach algebra $A$ implies the Arens regularity of certain Banach right module action of $A$ .
متن کاملA Hybrid Proximal Point Algorithm for Resolvent operator in Banach Spaces
Equilibrium problems have many uses in optimization theory and convex analysis and which is why different methods are presented for solving equilibrium problems in different spaces, such as Hilbert spaces and Banach spaces. The purpose of this paper is to provide a method for obtaining a solution to the equilibrium problem in Banach spaces. In fact, we consider a hybrid proximal point algorithm...
متن کاملFourier Multipliers and Periodic Solutions of Delay Equations in Banach Spaces
In this paper we characterize the existence and uniqueness of periodic solutions of inhomogeneous abstract delay equations and establish maximal regularity results for strong solutions. The conditions are obtained in terms of R-boundedness of linear operators determined by the equations and LFourier multipliers. Periodic mild solutions are also studied and characterized.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010