On L1 Space Formed by Complex-Valued Partial Functions
نویسندگان
چکیده
منابع مشابه
On L1 Space Formed by Complex-Valued Partial Functions
Let D be a non empty set and let E be a complex-membered set. One can verify that every element of D→̇E is complex-valued. Let D be a non empty set, let E be a complex-membered set, and let F1, F2 be elements of D→̇E. Then F1 + F2 is an element of D→̇C. Then F1 − F2 is an element of D→̇C. Then F1 · F2 is an element of D→̇C. Then F1/F2 is an element of D→̇C. Let D be a non empty set, let E be a comple...
متن کاملOn L Space Formed by Real-Valued Partial Functions
This article is the continuation of [31]. We define the set of L p integrable functions – the set of all partial functions whose absolute value raised to the p-th power is integrable. We show that L p integrable functions form the L p space. We also prove Minkowski's inequality, Hölder's inequality and that L p space is Banach space ([15], [27]). For simplicity, we follow the rules: X denotes a...
متن کاملOn L^1 Space Formed by Real-Valued Partial Functions
This article contains some definitions and properties refering to function spaces formed by partial functions defined over a measurable space. We formalized a function space, the so-called L space and proved that the space turns out to be a normed space. The formalization of a real function space was given in [16]. The set of all function forms additive group. Here addition is defined by point-...
متن کاملComplex Valued Functions Space
We adopt the following convention: x1, x2, z are sets, A is a non empty set, and f , g, h are elements of CA. Let us consider A. The functor +CA yielding a binary operation on CA is defined by: (Def. 1) For all elements f , g of CA holds +CA(f, g) = (+C)◦(f, g). Let us consider A. The functor ·CA yielding a binary operation on CA is defined as follows: (Def. 2) For all elements f , g of CA hold...
متن کاملConvolution Operators on Banach Space Valued Functions.
The purpose of this paper is to obtain systematically certain classical inequalities concerning the Hilbert transform, the function g of Littlewood and Paley, their generalizations to several variables, and related results.t This we accomplish by establishing certain inequalities for convolution operators on Banach space valued functions. Given a Banach space B, If I will denote the norm of the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Formalized Mathematics
سال: 2012
ISSN: 1898-9934,1426-2630
DOI: 10.2478/v10037-012-0039-4