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...

maximal operator M is a significant non-linear operator used in real analysis and harmonic analysis. The operator takes a locally integrable function...

and proved this by proving bounds on a circular maximal function analogous to the Kakeya maximal function. It was conjectured that there existed sets containing...

is in Lp(T). The function F defined on the unit disk by F(reiθ) = (f ∗ Pr)(eiθ) is harmonic, and M f  is the radial maximal function of F. When M f  belongs...

In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept...

Maximal inspiratory pressure (MIP) is the maximal pressure that can be produced by the patient trying to inhale through a blocked mouthpiece. Maximal...

r)}|f(y)|\,d\mu (y){\Bigr )}.} This maximal function is lower semicontinuous, hence measurable. The following maximal inequality is satisfied for every...

plane containing the closed unit disc D(0, 1). The radial maximal function for the function φ (restricted to the unit disc) is defined on the unit circle...

In the arts, maximalism is an aesthetic characterized by excess and abundance, serving as a reaction against minimalism. The philosophy can be summarized...

isomorphic to the standard torus Tn). A maximal torus is one which is maximal among such subgroups. That is, T is a maximal torus if for any torus T′ containing...

p equal to 1 or ∞. Another famous example is the Hardy–Littlewood maximal function, which is only sublinear operator rather than linear. While L p {\displaystyle...

analysis, the maximum and minimum of a function are, respectively, the greatest and least value taken by the function. Known generically as extremum, they...

a locally integrable function f—can be proved as a consequence of the weak–L1 estimates for the Hardy–Littlewood maximal function. The proof below follows...

V̇O2 max (also maximal oxygen consumption, maximal oxygen uptake or maximal aerobic capacity) is the maximum rate of oxygen consumption attainable during...

In mathematics, the Hausdorff maximal principle is an alternate and earlier formulation of Zorn's lemma proved by Felix Hausdorff in 1914 (Moore 1982:168)...

measuring of breath) is the most common of the pulmonary function tests (PFTs). It measures lung function, specifically the amount (volume) and/or speed (flow)...

In scale (music) theory, a maximally even set (scale) is one in which every generic interval has either one or two consecutive integers specific intervals-in...

described by some transfer function, "families" of special transfer functions are commonly used: Butterworth filter – maximally flat in passband and stopband...

choice of maximal commuting sets of observables for the abstract state space, there is a corresponding representation that is associated to a function space...

In mathematics, the error function (also called the Gauss error function), often denoted by erf, is a function e r f : C → C {\displaystyle \mathrm {erf}...

}}-{\sqrt {3}}} for x. By the implicit function theorem, each choice defines a function; for the first one, the (maximal) domain is the interval [−2, 2] and...

(that is, every totally ordered subset) necessarily contains at least one maximal element. The lemma was proved (assuming the axiom of choice) by Kazimierz...

Hardy–Littlewood maximal operator is bounded on Lp(dω). Specifically, we consider functions  f  on Rn and their associated maximal functions M( f ) defined...

definition Hardy–Littlewood inequality Hardy–Littlewood maximal function Hardy–Littlewood zeta function conjectures Hardy–Littlewood tauberian theorem First...

Half maximal inhibitory concentration (IC50) is a measure of the potency of a substance in inhibiting a specific biological or biochemical function. IC50...

Stein maximal principle (showing that under many circumstances, almost everywhere convergence is equivalent to the boundedness of a maximal function), Stein...

Hardy–Littlewood inequality Hardy–Littlewood maximal function Hardy–Littlewood tauberian theorem Hardy–Littlewood zeta function conjectures Hardy–Ramanujan Journal...

of Poisson integrals, interpolation theory and the Hardy–Littlewood maximal function. For more general operators, fundamental new techniques, introduced...

prime. A maximal order for Ω(n) is ln n / ln 2: 83  It is conjectured that the Mertens function, or summatory function of the Möbius function, satisfies...

Half maximal effective concentration (EC50) is a measure of the concentration of a drug, antibody or toxicant which induces a biological response halfway...