Sentence examples for maximal operator the from inspiring English sources

Applications to the Hardy Littlewood maximal operator, the Hilbert transform and composition of operators are also given.

For any maximal operator, the resolvent operator associated with, for any, is defined as (3.1).

See [2 6] for more results and applications for the sharp maximal operator, the Dirac operator, and Green's operator.

The boundedness of the Hardy-Littlewood maximal operator, the fractional integral operator, and the Calderón-Zygmund singular integral operator on Morrey space can be found in [11 15].

In [9], Chiarenza and Frasca showed the boundedness of the Hardy-Littlewood maximal operator, the fractional integral operator and the Calderón-Zygmund singular integral operator on Morrey spaces.

These conditions are satisfied by most of the operators in harmonic analysis, such as the Hardy-Littlewood maximal operator, the Calderón-Zygmund singular integral operator and so on.

The purpose of this paper is to estimate the Poincaré type inequalities for the composition of the maximal operator and the Green's operator over the -John domain.

In particular, we give new proofs, which completely avoid the good-λ inequalities, of Coifman's inequality relating singular integrals and the maximal operator, of the Fefferman Stein inequality relating the maximal operator and the sharp maximal operator, and the Muckenhoupt–Wheeden inequality relating the fractional integral operator and the fractional maximal operator.

We establish the Poincaré type inequalities for the composition of the maximal operator and the Green's operator in John domains.

We prove Lp boundedness for the maximal operator of the heat semigroup associated to the Laguerre functions, {Lαk}k, when the parameter α is greater than −1.

Furthermore, we obtain the boundedness of the maximal operator in the local Morrey-Lorentz spaces.