Integrability of Functions in the Space $L^{1}_{1}(\varOmega )$

2011 ◽  
pp. 287-321
Author(s):  
Vladimir Maz’ya
Keyword(s):  
Integrability Of Functions

scholarly journals Sharp Exponential Integrability for Traces of Monotone Sobolev Functions

2008 ◽  
Vol 192 ◽  
pp. 137-149 ◽  
Author(s):  
Pekka Pankka ◽  
Pietro Poggi-Corradini ◽  
Kai Rajala
Keyword(s):  
Unit Ball ◽  
Exponential Integrability ◽  
Geometric Methods ◽  
Sobolev Functions ◽  
Integrability Of Functions ◽  
Monotone Sobolev Functions

AbstractWe answer a question posed in [12] on exponential integrability of functions of restricted n-energy. We use geometric methods to obtain a sharp exponential integrability result for boundary traces of monotone Sobolev functions defined on the unit ball.

scholarly journals The (C, α) integrability of functions by weighted mean methods

Filomat ◽  
2012 ◽  
Vol 26 (6) ◽  
pp. 1209-1214 ◽  
Author(s):  
İbrahim Çanak ◽  
Ümit Totur
Keyword(s):  
Continuous Function ◽  
Weighted Mean ◽  
Integrability Of Functions

Let p(x) be a nondecreasing continuous function on [0, ?) such that p(0) = 0 and p(t) ? ? as t ? ?. For a continuous function f (x) on [0, ?), we define s(t)= ?0t f(u)du and ?? (t) =?0t? (1- p(u)/p(t))? f(u)du. We say that a continuous function f (x) on [0, ?) is (C, ?) integrable to a by the weighted mean method determined by the function p(x) for some ? > ?1 if the limit limt?? ?? (t) = a exists. We prove that if the limit limt?? ?? (t) = a exists for some ? > ?1, then the limit limt?? ??+h (t) = a exists for all h > 0. Next, we prove that if the limit limt?? ?? (t) = a exists for some ? > 0 and p(t)/p?(t) f(t)= O(1), t ? ?, then the limit limt?? ???1 (t) = a exists.

scholarly journals General criteria of integrability of functions of passage-times for non-negative stochastic processes and their applications

1998 ◽  
Vol 43 (3) ◽  
pp. 509-539 ◽  
Author(s):  
Sanjar Aspandiiarov ◽  
Sanjar Aspandiiarov ◽  
Р Ясногородский ◽  
R Iasnogorodski
Keyword(s):  
Stochastic Processes ◽  
Integrability Of Functions ◽  
Passage Times

scholarly journals On weighted integrability of functions defined by trigonometric series with p-bounded variation coefficients

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Bogdan Szal ◽  
Maciej Kubiak
Keyword(s):  
Trigonometric Series ◽  
Bounded Variation ◽  
Necessary Condition ◽  
Integrability Of Functions ◽  
Sufficient And Necessary Condition ◽  
Weighted Integrability

Abstract In this paper we introduce new classes of p-bounded variation sequences and give a sufficient and necessary condition for weighted integrability of trigonometric series with coefficients belonging to these classes. This is a generalization of the results obtained by the first author [J. Inequal. Appl. 2010:1–19, 2010] and Dyachenko and Tikhonov [Stud. Math. 193(3):285–306, 2009].

scholarly journals The Multiple K -Riemann Integral

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Oussama Kabbouch ◽  
Mustapha Najmeddine
Keyword(s):  
Riemann Integral ◽  
Equivalent Definition ◽  
Step Functions ◽  
Integrable Functions ◽  
Riemann Integrable Functions ◽  
Integrability Of Functions ◽  
Definition Of

The aim of this paper is to extend the notion of K -Riemann integrability of functions defined over a , b to functions defined over a rectangular box of ℝ n . As a generalization of step functions, we introduce a notion of K -step functions which allows us to give an equivalent definition of the K -Riemann integrable functions.

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