On a Relationship between the Integrabilities of Various Maximal Functions
نویسنده
چکیده
It is shown that the right-sided, left-sided, and symmetric maximal functions of any measurable function can be integrable only simultaneously. The analogous statement is proved for the ergodic maximal functions. Introduction. We deal with integrable functions on T = [0, 2π) and assume that they are extended to 2π-periodic functions on the whole line R. The class of such functions will be denoted by L. One can also consider the functions of L to be defined on the unit circle in the complex plane. If a measurable set E ⊂ R is such that IE is a 2π-periodic function and f ∈ L, then we assume that |E| = νE = ν(E ∩ T) and
منابع مشابه
A Conceptual Model on Relationship between Structure and Functions in Rangeland Ecosystems
One of the most important issues in structure-function relationship modeling is that each rangeland has numerous functions and each of them can provide the most benefits in a certain state of that ecosystem. In fact, relationship between structure and function can be varied in different states. After presentation of the Linear Structure-Function Model based on the Clementsian succession theory,...
متن کاملON MAXIMAL IDEALS OF R∞L
Let $L$ be a completely regular frame and $mathcal{R}L$ be the ring of real-valued continuous functions on $L$. We consider the set $$mathcal{R}_{infty}L = {varphi in mathcal{R} L : uparrow varphi( dfrac{-1}{n}, dfrac{1}{n}) mbox{ is a compact frame for any $n in mathbb{N}$}}.$$ Suppose that $C_{infty} (X)$ is the family of all functions $f in C(X)$ for which the set ${x in X: |f(x)|geq dfrac{1...
متن کاملSome results on fuzzy semi maximal filters in BL-algebras
In this paper, first, the concept of the fuzzy semi maximal filters in BL-algebras has been introduced, then several properties of fuzzy semi maximal filters have been studied and its relationship with other fuzzy filters including fuzzy (positive)implicative fuzzy filters and fuzzy fantastic filters are investigated. In the following, using the level subsets of fuzzy sets in a BL-algebra...
متن کاملOn semi maximal filters in BL-algebras
In this paper, first we study the semi maximal filters in linear $BL$-algebras and we prove that any semi maximal filter is a primary filter. Then, we investigate the radical of semi maximal filters in $BL$-algebras. Moreover, we determine the relationship between this filters and other types of filters in $BL$-algebras and G"{o} del algebra. Specially, we prove that in a G"{o}del algebra, any ...
متن کاملPartial second-order subdifferentials of -prox-regular functions
Although prox-regular functions in general are nonconvex, they possess properties that one would expect to find in convex or lowerC2 functions. The class of prox-regular functions covers all convex functions, lower C2 functions and strongly amenable functions. At first, these functions have been identified in finite dimension using proximal subdifferential. Then, the definition of prox-regula...
متن کامل