Sentence examples for maximal operator of from inspiring English sources

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.

For differential form u ∈ L s ( B 0, Λ l ), 1 ≤ s < ∞, l = 0, 1, …, n, the Hardy-Littlewood maximal operator of order s is defined by.

Later, Strömberg [14] gave a simple proof, adopting the idea of relating commutators with the sharp maximal operator of Fefferman and Stein.

Notice that for β = 0 the previous definition gives back the classical sharp maximal operator of Fefferman and Stein (in the restricted version), which is in fact denoted by M R # ( f ).

Weisz [9] proved that the maximal operator of the Fejér means (sigma^{ast }) is bounded from the Hardy space (H_{1/2}) to the space weak-(L_{1/2}).

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.

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

We give complete descriptions of the various spectra of the minimal and maximal operators of the Laplacian on the upper half space and the unit ball.

We prove and discuss some new (H_{p} -(L_{p}) type inequalities of weighted maximal operators of Vilenkin-Nörlund means with monotone coefficients.

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).

There Theorem 8 is actually obtained as a corollary of a more general estimate for certain maximal operators of D u. From the discussion made there it will be clear that the points x, y are Lebesgue points of u when the right hand side in (33) is finite; compare with Remark 1.