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searching for Locally integrable function 15 found (33 total)

alternate case: locally integrable function

Radial function (451 words) [view diff] no match in snippet view article find links to article

\rho ]} for every test function φ and rotation ρ. Given any (locally integrable) function f, its radial part is given by averaging over spheres centered

Distribution (mathematics) (21,579 words) [view diff] exact match in snippet view article

derivatives do not exist in the classical sense. In particular, any locally integrable function has a distributional derivative. Distributions are widely used

Frederick Gehring (820 words) [view diff] exact match in snippet view article find links to article

following lemma: Assume that f {\displaystyle f} is a non–negative locally integrable function on Rn and 1 < p {\displaystyle p} < ∞. If there is a constant

Maximal function (1,467 words) [view diff] exact match in snippet view article find links to article

( M f ) ( x ) {\displaystyle F^{*}(x)\leq C(Mf)(x)} . For a locally integrable function f on Rn, the sharp maximal function f ♯ {\displaystyle f^{\sharp

Hardy–Littlewood maximal function (1,890 words) [view diff] exact match in snippet view article find links to article

in real analysis and harmonic analysis. The operator takes a locally integrable function f : R d → C {\displaystyle f:\mathbb {R} ^{d}\to \mathbb {C}

Muckenhoupt weights (1,674 words) [view diff] exact match in snippet view article find links to article

above definition. (b) There is a constant c such that for any locally integrable function f on Rn, and all balls B: ( f B ) p ≤ c ω ( B ) ∫ B f ( x )

Weyl's lemma (Laplace equation) (2,271 words) [view diff] exact match in snippet view article

denote the usual Laplace operator. Weyl's lemma states that if a locally integrable function u ∈ L l o c 1 ( Ω ) {\displaystyle u\in L_{\mathrm {loc} }^{1}(\Omega

Calculus on Euclidean space (11,455 words) [view diff] exact match in snippet view article find links to article

to give sense to a derivative of such a function. Note each locally integrable function u {\displaystyle u} defines the linear functional φ ↦ ∫ u φ d

Kakeya set (3,697 words) [view diff] exact match in snippet view article find links to article

parallel to the direction of the unit vector e ∈ Sn−1. Then for a locally integrable function f, we define the Kakeya maximal function of f to be f ∗ δ ( e

Real analysis (7,670 words) [view diff] exact match in snippet view article find links to article

derivatives do not exist in the classical sense. In particular, any locally integrable function has a distributional derivative. Real analysis is an area of

Two-sided Laplace transform (1,995 words) [view diff] exact match in snippet view article find links to article

The region of convergence will be normally smaller. If f is a locally integrable function (or more generally a Borel measure locally of bounded variation)

Laplace transform (9,705 words) [view diff] exact match in snippet view article find links to article

the related difficulties with proving convergence). If f is a locally integrable function (or more generally a Borel measure locally of bounded variation)

Fourier transform (21,320 words) [view diff] exact match in snippet view article find links to article

be found by differentiating 320. If Re α > −1, then |x|α is a locally integrable function, and so a tempered distribution. The function α ↦ |x|α is a holomorphic

Beltrami equation (10,947 words) [view diff] exact match in snippet view article find links to article

z , {\displaystyle \displaystyle {E(z)={1 \over \pi z},}} a locally integrable function on C. Thus on Schwartz functions f ∂ z ¯ ( E ⋆ f ) = f . {\displaystyle

Spaces of test functions and distributions (18,954 words) [view diff] exact match in snippet view article find links to article

measure becomes a distribution on U. If f {\displaystyle f} is a locally integrable function on U then the distribution ϕ ↦ ∫ U f ( x ) ϕ ( x ) d x {\displaystyle