Abstract We study the size of shadow k -uniform hypergraphs with bounded degree. Lower bounds on ratio and hypergraph are given as a function degree bound . show that cliques extremal for long range bounds, but not every bound. give general, sharp lower show, sometimes we can get by deleting disjoint maximal matchings from clique

Let Sα,ψ( f ) be the square function defined by means of the cone in R n+1 + of aperture α, and a standard kernel ψ . Let [w]Ap denote the Ap characteristic of the weight w. We show that for any 1 < p < ∞ and α ≥ 1, ‖Sα,ψ‖L p(w) αn[w] max ( 1 2 , 1 p−1 ) Ap . For each fixed α the dependence on [w]Ap is sharp. Also, on all class Ap the result is sharp in α. Previously this estimate was proved in...

Technical limitations in image capturing usually impose defective, such as contrast degradation. There are different approaches to improve the contrast of an image. Among the exiting approaches, un-sharp masking is a popular method due to its simplicity in implementation and computation. There is an important parameter in un-sharp masking, named gain factor, which affects the quality of the enh...

Suppose D is a bounded C domain in R and GD is the Green function of the killed symmetric α-stable process in D. In this note we establish a sharp upper bound estimate for GD in such a way that the explicit dependence of the constant in the estimate on α is also given. This sharp estimate allows us to recover the sharp upper bound estimate for the Green function of killed Brownian motion in D b...

We find the sharp range for boundedness of discrete bilinear spherical maximal function dimensions $d \geq 5$. That is, we show that this operator is bounded on $l^{p}(\mathbb{Z}^d)\times l^{q}(\mathbb{Z}^d) \to l^{r}(\mathbb{Z}^d)$ $\frac{1}{p} + \frac{1}{q} \frac{1}{r}$ and $r>\frac{d}{2d-2}$ sharp. Our approach mirrors used by Jeong Lee in continuous setting. For $d=3,4$, our previous work, ...