Sentence examples for maximal function for from inspiring English sources
Our proofs are based on the investigation of a new maximal function for spherical polynomials.
To do so, we develop various vector-valued analogues of classical objects in Harmonic Analysis, including a maximal function for Bochner spaces.
In 1986, Burkholder explicitly found the maximal function for (p=2).
In 1986, Burkholder explicitly found the maximal function for (p=2) without the realization of this structural property of this type of extremal functions.
In [6], Bekjan defined the Hardy-Littlewood maximal function for τ-measurable operators and, among other things, obtained weak ( 1, 1 ) -type and ( p, p ) -type inequalities for the Hardy-Littlewood maximal function.
"My guess is that our neurons basically do the best they can to maintain maximal functioning for as long as they can," Sherwood says.
As for the maximal operator σ ∗ given by (2.2), we invoke the following lemma in [[21], Lemma 3.2]: We define the directional Hardy-Littlewood maximal function of F for a fixed vector y ′ ∈ S n − 1 by M y ′ F ( x ) = sup r > 0 1 2 r ∫ − r r | f ( x − t y ′ ) | d t.
For a locally integrable function f, let (M^f) be the sharp maximal function of f, namely, for (xinmathcal{X}), M^f(x)=sup_{xin B}frac{1}{mu 6B }int _{B}biglvert f y -m_{tilde{B}}f y -m_{tilde{(y)+ sup_{(B}}fbigrvert{x}}frac{vert m_{B}f-m_{S}fvert }{K_{B,dmu, (2.1) where (Delta_{x}={(B,S):xin Bsubset S mbox{ and } B, S mbox{ are doubling balls}}).
In the present study, the effects of culture conditions on the net photosynthetic rate of a rootless submerged plant, Ceratophyllum demersum L., was investigated to determine the optimum culture conditions for maximal function of plants in food production modules including both aquatic plant culture and fish culture systems.
We also show that nanU is required for maximal function of the transport system and that it is expressed in a sialic acid-responsive manner.
And the pointwise estimate for the sharp maximal function of commutators generated by strongly singular Calderón-Zygmund operandrs and BMO functions was also established.
