scholarly journals On Lp Space Formed by Real-Valued Partial Functions

2010 ◽  
Vol 18 (3) ◽  
pp. 159-169
Author(s):  
Yasushige Watase ◽  
Noboru Endou ◽  
Yasunari Shidama
Keyword(s):  
Banach Space ◽  
Hölder’S Inequality ◽  
Minkowski’S Inequality ◽  
Partial Functions ◽  
Lp Space ◽  
Hölder's Inequality ◽  
Absolute Value ◽  
Integrable Functions

On Lp Space Formed by Real-Valued Partial Functions This article is the continuation of [31]. We define the set of Lp integrable functions - the set of all partial functions whose absolute value raised to the p-th power is integrable. We show that Lp integrable functions form the Lp space. We also prove Minkowski's inequality, Hölder's inequality and that Lp space is Banach space ([15], [27]).

scholarly journals TENSOR PRODUCT REPRESENTATION OF THE (PRE)DUAL OF THE Lp-SPACE OF A VECTOR MEASURE

2009 ◽  
Vol 87 (2) ◽  
pp. 211-225 ◽  
Author(s):  
IRENE FERRANDO ◽  
ENRIQUE A. SÁNCHEZ PÉREZ
Keyword(s):  
Banach Space ◽  
Tensor Product ◽  
Normed Space ◽  
Dual Space ◽  
Vector Measure ◽  
Real Numbers ◽  
Product Representation ◽  
Lp Space ◽  
Integrable Functions ◽  
Tensor Product Representation

AbstractThe duality properties of the integration map associated with a vector measure m are used to obtain a representation of the (pre)dual space of the space Lp(m) of p-integrable functions (where 1<p<∞) with respect to the measure m. For this, we provide suitable topologies for the tensor product of the space of q-integrable functions with respect to m (where p and q are conjugate real numbers) and the dual of the Banach space where m takes its values. Our main result asserts that under the assumption of compactness of the unit ball with respect to a particular topology, the space Lp(m) can be written as the dual of a suitable normed space.

scholarly journals Hölder inequality for functions that are integrable with respect to bilinear maps

2008 ◽  
Vol 102 (1) ◽  
pp. 101 ◽  
Author(s):  
O. Blasco ◽  
J. M. Calabuig
Keyword(s):  
Banach Space ◽  
Measure Space ◽  
Hölder’S Inequality ◽  
Finite Measure ◽  
Hölder Inequality ◽  
Bilinear Maps ◽  
Bilinear Map ◽  
Hölder's Inequality ◽  
Finite Measure Space

Let $(\Omega, \Sigma, \mu)$ be a finite measure space, $1\le p<\infty$, $X$ be a Banach space $X$ and $B:X\times Y \to Z$ be a bounded bilinear map. We say that an $X$-valued function $f$ is $p$-integrable with respect to $B$ whenever $\sup_{\|y\|=1} \int_\Omega \|B(f(w),y)\|^p\,d\mu<\infty$. We get an analogue to Hölder's inequality in this setting.

scholarly journals On Some Inequalities for the Chaudhry-Zubair Extension of the Gamma Function

2019 ◽  
pp. 1-9
Author(s):  
Monica Atogpelge Atugba ◽  
Kwara Nantomah
Keyword(s):  
Gamma Function ◽  
Hölder’S Inequality ◽  
Minkowski’S Inequality ◽  
Young’S Inequality ◽  
Hölder's Inequality ◽  
Analytical Tools ◽  
Young's Inequality

By applying the classical Holder's inequality, Young's inequality, Minkowski's inequality and some other analytical tools, we establish some inequalities involving the Chaudhry-Zubair extension of the gamma function. The established results serve as generalizations of some known results in the literature.

scholarly journals Hilbert-type inequalities for time scale nabla calculus

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
H. M. Rezk ◽  
Ghada AlNemer ◽  
H. A. Abd El-Hamid ◽  
Abdel-Haleem Abdel-Aty ◽  
Kottakkaran Sooppy Nisar ◽  
...  
Keyword(s):  
Time Scale ◽  
Hölder’S Inequality ◽  
Hölder's Inequality ◽  
Arbitrary Time ◽  
Hilbert Type

Abstract This paper deals with the derivation of some new dynamic Hilbert-type inequalities in time scale nabla calculus. In proving the results, the basic idea is to use some algebraic inequalities, Hölder’s inequality, and Jensen’s time scale inequality. This generalization allows us not only to unify all the related results that exist in the literature on an arbitrary time scale, but also to obtain new outcomes that are analytical to the results of the delta time scale calculation.

scholarly journals On Simultaneous Farthest Points in

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
Sh. Al-Sharif ◽  
M. Rawashdeh
Keyword(s):  
Banach Space ◽  
Bounded Subset ◽  
Farthest Points ◽  
Integrable Functions

Let be a Banach space and let be a closed bounded subset of . For , we set  . The set is called simultaneously remotal if, for any , there exists such that  . In this paper, we show that if is separable simultaneously remotal in , then the set of -Bochner integrable functions, , is simultaneously remotal in . Some other results are presented.

scholarly journals Best Simultaneous Approximation in Orlicz Spaces

2007 ◽  
Vol 2007 ◽  
pp. 1-7 ◽  
Author(s):  
M. Khandaqji ◽  
Sh. Al-Sharif
Keyword(s):  
Banach Space ◽  
Simultaneous Approximation ◽  
Closed Subspace ◽  
Orlicz Spaces ◽  
Unit Interval ◽  
Luxemburg Norm ◽  
Integrable Functions ◽  
Best Simultaneous Approximation ◽  
Distance Formula

LetXbe a Banach space and letLΦ(I,X)denote the space of OrliczX-valued integrable functions on the unit intervalIequipped with the Luxemburg norm. In this paper, we present a distance formula dist(f1,f2,LΦ(I,G))Φ, whereGis a closed subspace ofX, andf1,f2∈LΦ(I,X). Moreover, some related results concerning best simultaneous approximation inLΦ(I,X)are presented.

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