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 partial differential equations. They often provide a deeper and more simplified approach to understanding problems in these areas than other methods.
Maximalfunctions appear in many forms in harmonic analysis (an area of mathematics). One of the most important of these is the Hardy–Littlewood maximal...
and proved this by proving bounds on a circular maximalfunction analogous to the Kakeya maximalfunction. It was conjectured that there existed sets containing...
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept...
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 maximalfunction of F. When M f belongs...
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 maximalfunction is lower semicontinuous, hence measurable. The following maximal inequality is satisfied for every...
plane containing the closed unit disc D(0, 1). The radial maximalfunction for the function φ (restricted to the unit disc) is defined on the unit circle...
In the arts, maximalism, a reaction against minimalism, is an aesthetic of excess. The philosophy can be summarized as "more is more", contrasting with...
p equal to 1 or ∞. Another famous example is the Hardy–Littlewood maximalfunction, which is only sublinear operator rather than linear. While L p {\displaystyle...
V̇O2 max (also maximal oxygen consumption, maximal oxygen uptake or maximal aerobic capacity) is the maximum rate of oxygen consumption attainable during...
a locally integrable function f—can be proved as a consequence of the weak–L1 estimates for the Hardy–Littlewood maximalfunction. The proof below follows...
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...
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 defined as: erf z = 2 π ∫ 0 z e − t 2...
analysis, the maximum and minimum of a function are, respectively, the largest and smallest value taken by the function. Known generically as extremum, they...
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)...
described by some transfer function, "families" of special transfer functions are commonly used: Butterworth filter – maximally flat in passband and stopband...
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...
Half maximal inhibitory concentration (IC50) is a measure of the potency of a substance in inhibiting a specific biological or biochemical function. IC50...
Hardy–Littlewood maximal operator is bounded on Lp(dω). Specifically, we consider functions f on Rn and their associated maximalfunctions M( f ) defined...
of Poisson integrals, interpolation theory and the Hardy–Littlewood maximalfunction. For more general operators, fundamental new techniques, introduced...
Half maximal effective concentration (EC50) is a measure of the concentration of a drug, antibody or toxicant which induces a biological response halfway...
vertices), finding a maximum weight clique in a weighted graph, listing all maximal cliques (cliques that cannot be enlarged), and solving the decision problem...
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