Sentence examples for maximal operator on from inspiring English sources

In this note I present a sufficient condition for the boundedness of the maximal operator on generalized Orlicz spaces.

We investigate the square variation operator V2 (which majorizes the partial sum maximal operator) on general orthonormal systems (ONS) of size N.

We next state the relation between the generalized Muckenhoupt conditions and the boundedness of the Hardy-Littlewood maximal operator on weighted Lebesgue spaces in the variable exponent setting.

The conditions on variable exponents have been established by the study of the boundedness of the Hardy-Littlewood maximal operator on spaces with variable exponent [2 8].

Suppose that 1 ≤ p < ∞, and M is the maximal operator on Lp(G) defined by a sequence {ψn}∞n = 1 of strong type Fourier multipliers which are continuous functions on γ.

In particular, Cruz-Uribe, Fiorenza and Neugebauer [17] and Diening and Hästö [18] have independently proved the equivalence between the Muckenhoupt condition and the boundedness of the Hardy-Littlewood maximal operator on weighted Lebesgue spaces in the variable exponent setting.

We will introduce the times modified centered and uncentered Hardy-Littlewood maximal operators on nonhomogeneous spaces for.

We will also prove other results of Hardy-Littlewood maximal operators on homogeneous spaces and on the real line by using outer measures.

We study the following well-known property of the dyadic maximal operator Md on Rn (see [E.M. Stein, Note on the class LlogL, Studia Math.

Our main result establishes that M is of weak type (p, p) on Lp(G) if and only if the corresponding maximal operator M# on Lp(b(G)) is of weak type (p, p).

In the following section, we will study the boundedness of maximal operator (M_{Omega}) on Morrey and modified Morrey spaces.