Sentence examples for maximal function on from inspiring English sources

The classical Nikodym maximal function on the Euclidean plane R2 is defined as the supremum over averages over rectangles of eccentricity N; its operator norm in L2(R2) is known to be O logN).

We also establish that the Hardy space H1 ˜X) is a sum of finitely many dyadic Hardy spaces on ˜X, and that the strong maximal function on ˜X is pointwise comparable to the sum of finitely many dyadic strong maximal functions.

For a family of weight functions invariant under a finite reflection group, the boundedness of a maximal function on the unit sphere is established and used to prove a multiplier theorem for the orthogonal expansions with respect to the weight function on the unit sphere.

In this paper, we study the Hardy-Littlewood maximal function on noncommutative Lorentz spaces.

For and, the sharp maximal function on is defined by (2.1).

This paper is mainly devoted to the study of the Hardy-Littlewood maximal function on noncommutative Lorentz spaces and to obtaining ( p, q ) - ( p, q ) -type inequality for the Hardy-Littlewood maximal function on noncommutative Lorentz spaces.

Muckenhoupt [27] firstly introduced the theory of (A_{p}) weights while studying Hardy-Littlewood maximal functions on weighted (L^{p}) spaces.

We have the following result taken from [9] that characterizes the boundedness of these maximal functions on L p (ℝ n ).

For λ ∈ ( 0, 1 ) and a measurable function f on R n, the local sharp maximal function of f is defined by M λ # ( f ) ( x ) = sup Q ∋ x inf c ∈ C ( ( f − c ) χ Q ) ∗ ( λ | Q | ).

For λ ∈ ( 0, 1 ) and the measurable function f on R n, the local sharp maximal function of f is defined by M λ # ( f ) ( x ) = sup Q ∋ x inf c ∈ C ( ( f − c ) χ Q ) ∗ ( λ | Q | ).

Our proofs are based on the investigation of a new maximal function for spherical polynomials.