Sentence examples for maximal operator with from inspiring English sources
On the other hand, we shall study the boundedness of the multilinear fractional maximal operator with a weighted norm.
where M u is the maximal operator with respect to udσ, the second inequality follows from the doubling condition of udσ.
When (mathcal{B}_{x}) denotes the collection of all rectangles R containing (xinmathbb{R}^{n}) whose sides parallel to the coordinate axes, (mathcal{M}triangleq M_{dnu}^{n}) is the strong maximal operator with respect to measure ν in dimension n.
For a one-dimensional Hardy-Littlewood maximal operator with respect to the measure (omega_{x_{2}},dmu_{1}), it is well known that (M_{omega_{x_{2}},dmu_{1}}) is bounded on (L^{2} omega_{x_{2}},dmu_{1})) [10], which implies that omega_{x_{2}} biggl(bigcup_{i}I_{i} biggr)leq c omega_{x_{2}} Bigl(bigcuphat {I}_{i}^{ast} Bigr).
In this article, we study necessary and sufficient conditions on the parameters of the boundedness on Morrey spaces and modified Morrey spaces for (T_{Omega,alpha}) and (M_{Omega,alpha}), which are a multilinear fractional integral and a multilinear fractional maximal operator with rough kernel, respectively.
We also obtain the corresponding weighted vector-valued inequalities for these operators and for the maximal operator associated with a starlike set.
In this paper we investigate the endpoint regularity of the discrete m-sublinear fractional maximal operator associated with (ell^{1} -balls, both in the centered and uncentered versions.
The maximal operator associated with T is T max = T 0 ∗, where D ( T max ) = { F ∈ ( L 2 ( 0, ∞ ) ) 2 ∣ F, F ′ ∈ A C }.
Given a Young function φ, we define the Orlicz maximal operator associated with φ by M φ u ( x ) = sup Q ∍ x ∥ u ∥ φ ( Q ).
The operator (L_{0}) defined by D(L_{0})=W_{2}^{n}(0,a), quadquad L_{0}y=ell y, quad yin W_{2}^{n}(0,a), (2.2) is called the maximal operator associated with the differential expression ℓ on ([0,a]).
(1.3) Define the local maximal operator associated with the family of operators ({S_{t,a}}_{0< t<1}) by S^{ast}_{a}f(x)= sup_{0< t< 1}biglvert S_{t,a}f(x bigrvert, quad xin mathbb{R}^{n}.
