Strong maximal function
WebMar 17, 2024 · The strong maximal function is one of the most important operators in the theory of multi-parameter singular integrals, associated with which is an underlying non … WebMB2(0) the strong maximal operator corresponding to the frame 0. By B1(x) (x e Rn) we denote a family of all cubic intervals in Rn con-taining x (for n = 1 a one-dimensional interval is understood here as a square interval). The support {x e Rn: f(x) = 0} of the function f : Rn-> R will be denoted by supp f. 2.
Strong maximal function
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WebOct 20, 2015 · With that, a subharmonic function should satisfy the maximum principle, the strong one, i.e. if there is x 0 ∈ Ω for which the maximum on Ω ¯ is u ( x 0), then u is constant. The proof uses a connection argument. Let Ω M = { x ∈ Ω ¯: u ( x) = M = u ( x 0) }. Then x 0 ∈ Ω M so Ω M ≠ ∅.
WebNov 22, 2016 · Weak type estimates for strong maximal functions were first studied by Jessen, Marcinkiewcz and Zygmund who first proved the strong differentiation theorem. … Webthe maximal operator for these more geometrically complicated objects is still a major challenge in harmonic analysis, leading to important open conjectures such as the …
WebTHE MULTILINEAR STRONG MAXIMAL FUNCTION LOUKAS GRAFAKOS, LIGUANG LIU, CARLOS PEREZ, RODOLFO H. TORRES´ Abstract. A multivariable version of the strong maximal function is introduced and a sharp distributional estimate for this operator in the spirit of the Jessen, Marcinkiewicz, and Zygmund theorem is obtained. Conditions that … WebA complex-valued harmonic function of which the absolute value has a maximum point is constant 1 Does the this converse of the MVT hold true for harmonic functions?
Maximal functions appear in many forms in harmonic analysis (an area of mathematics). One of the most important of these is the Hardy–Littlewood maximal function. They play an important role in understanding, for example, the differentiability properties of functions, singular integrals and … See more In their original paper, G.H. Hardy and J.E. Littlewood explained their maximal inequality in the language of cricket averages. Given a function f defined on R , the uncentred Hardy–Littlewood maximal function Mf of f is … See more Let $${\displaystyle (X,{\mathcal {B}},m)}$$ be a probability space, and T : X → X a measure-preserving endomorphism of X. The maximal function of f ∈ L (X,m) is The maximal … See more The non-tangential maximal function takes a function F defined on the upper-half plane $${\displaystyle \mathbf {R} _{+}^{n+1}:=\left\{(x,t)\ :\ x\in \mathbf {R} ^{n},t>0\right\}}$$ and produces a … See more 1. ^ Stein, Elias (1993). "Harmonic Analysis". Princeton University Press. 2. ^ Grakakos, Loukas (2004). "7". Classical and Modern Fourier … See more
WebFor the strong maximal function defined in terms of rectangles in Rn with sides parallel to the coordinate axes it was shown in [4] that weak Lp bounds are equivalent to certain ... maximal function by a careful analysis of collections of annuli. This paper is organized as follows. Proposition 1.1 illustrates how maximal function brian dawkins throwback jerseyWebstrong maximal function. Unfortunately, much of their proof was omitted and the estimate given is incorrect. We correct the estimate and give a direct proof using rearrangements, … coupons for medifast dietWebJun 10, 2014 · of the strong maximal function and some other more general maximal functions. We define the strong multilinear maximal function as m 1 r R3xfJ[ \K\ Jr X e R" where / = (/ι, · · · , fm) is an m-dimensional vector of locally integrable functions and where the supremum is taken over all rectangles with sides parallel to the coordinate axes. brian day artistWebWe recall that a strong maximal inequality is an L p-norm inequality for the maximal function, of the form ‖ M μ * f ‖ p ≤ C p ‖ f ‖ p, ∀ f ∈ L p (X), where 1 < p ≤ ∞. A weak-type maximal inequality is an estimate of the distribution function … brian dawkins pro bowlsThis theorem of G. H. Hardy and J. E. Littlewood states that M is bounded as a sublinear operator from the L (R ) to itself for p > 1. That is, if f ∈ L (R ) then the maximal function Mf is weak L -bounded and Mf ∈ L (R ). Before stating the theorem more precisely, for simplicity, let {f > t} denote the set {x f(x) > t}. Now we have: Theorem (Weak Type Estimate). For d ≥ 1, there is a constant Cd > 0 such that for all λ > 0 and f … coupons for meijer groceryWebMay 6, 2016 · In this paper, we establish the boundedness of strong maximal operator on mixed-norm Banach function spaces introduced in [ 4 ]. Our main result provides a unified principle for the boundedness of the strong maximal operator on the mixed-norm Lorentz spaces, the mixed-norm Orlicz spaces and the mixed-norm Lebesgue spaces with variable … coupons for melin hatsWebIf one forms a maximal function Ms;t by averaging over rectangles in IR3 with sidelengths s t st, then Ms;t is clearly dominated by M3,the strong maximal function in IR3. However, it turns out that the maximal function Ms;t associated to this dilation structure behaves more like M2, the two-dimensional strong maximal function. coupons for medtronic diabetes supplies