Sentence examples for maximal operators do from inspiring English sources

In dimension d="1 we prove that these maximal operators do not increase the Lp-variation of a function for any p⩾1, while in dimensions d>1 we obtain the corresponding results for the L2-variation.

The dental operators did the recording.

Of the initial 21 dental operators, 8 operators did not use ART after training [ 17].

Image analyses were conducted based on operator availability; operators did not use image registration to evaluate repeated scans.

Generally speaking, the spherical averaging operator has better properties than the rectangle averaging operator does, such as the Hardy-Littlewood maximal function.

As a corollary, we also give a generalization of the result of Sogge and Stein that for some finite p the maximal operator corresponding to a hypersurface whose Gaussian curvature does not vanish to infinite order is bounded on Lp for some finite p. Analogous estimates are proven for Fourier transforms of surface measures, and these are sharp for the same hypersurfaces as the maximal operators.

In this paper we study the regularity properties of two maximal operators of convolution type: the heat flow maximal operator (associated to the Gauss kernel) and the Poisson maximal operator (associated to the Poisson kernel).

We derive weighted norm estimates for integral operators of potential type and for their related maximal operators.

For example, Hardy operators, Hardy-Littlewood maximal operators, fractional integral operators, fractional maximal operators are admissible on ℝ (see [31]).

For instance: Hardy operators, Hardy-Littlewood maximal operators, Riemann-Liouville, and Weyl fractional integral operators, maximal fractional operators, etc.

There are, then, as many observables and kinds of physical properties for an operator f(Q) as there are ways to construct f(Q) from maximal operators.