Sentence examples for maximal operator and from inspiring English sources

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.

Examples include homogeneous singular integral operators with kernels which do not necessarily satisfy a Dini condition as well as several operators whose measures are supported on lower dimensional sets, such as the discrete spherical maximal operator and the Hilbert transform along a homogeneous curve.

We recall the definition of Hardy-Littlewood maximal operator and fractional maximal operator.

The continuity of fractional maximal operator and Bessel potential operator is discussed in [8] and [9].

Now we define the truncated centered Hardy-Littlewood maximal operator and the truncated uncentered Hardy-Littlewood maximal operator.

We will introduce two important operators including the Hardy-Littlewood maximal operator and the Calderón-Zygmund singular integral operator.

It is well-known that estimates for maximal operators and questions of pointwise convergence are strongly connected.

Radial maximal operators for suitable dilations, the heat and Poisson maximal operators, and the Riesz transform, which act onK-bi-invariant functions onG, satisfy theLp-norm inequalities forp>1 and a weak typeL1estimate.

Here we collect the definitions of commutators for the one-sided Hardy-Littlewood maximal operators and the one-sided Calderón-Zygmund singular integral operators as follows.

On the other hand, Rakotondratsimba ([5]) characterized some weighted inequalities in amalgams (corresponding to the cases and ) for the fractional maximal operators and the fractional integrals.

In this article, we characterize the pairs (u, v) of positive measurable functions such that T maps the weighted amalgam in (L p (u), ℓ q ) for all, where T belongs to a class of positive operators which includes Hardy operators, maximal operators, and fractional integrals.