Sentence examples for maximal function of from inspiring English sources

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.

Consider an elliptic second-order divergence operator L (including a boundary condition on ∂Ω) and define a Hardy space by imposing the non-tangential maximal function of the extension of a function f via the Poisson semigroup for L to be in L1.

When (xin B a,R)), we consider the uncentered Hardy-Littlewood maximal function of f at the point x.

The maximal function of a martingale f is defined by f^{ast}=sup_{nin mathbb{N}} biglvert f^{(n)} bigrvert.

And the pointwise estimate for the sharp maximal function of commutators generated by strongly singular Calderón-Zygmund operandrs and BMO functions was also established.

The Hardy-Littlewood maximal function of f is defined by M f ( x ) = sup r > 0 1 | B ( x, r ) | ∫ B ( x, r ) | f ( y ) | d y.

First, we derive the inequality between two sharp maximal functions of K f and f.

In 2011, the pointwise estimates for the sharp maximal functions of commutators generated by generalized Calderón-Zygmund operators and BMO functions or Lipschitz functions were established in [9].

It is the phosphorylation of serine 727, which in the nucleus is required for maximal transcriptional stimulation, that is important in both the Ras transformation of cells as well as in the maximal functioning of mitochondrial oxidative phosphorylation.

We need the following maximal function estimate of ([b, T_{beta}]).

On the other hand, Meda et al. [33] independently obtained some similar results by grand maximal function characterizations of Hardy spaces on R n.