Estimates for maximal functions associated to hypersurfaces in $\mathbb {R}^3$ with height $h<2$: Part I

Coefficient Estimates for Some Subclasses of Analytic and Bi-Univalent Functions Associated with Conic Domain

The main objective of this investigation is to introduce certain new subclasses of the class $Sigma $ of bi-univalent functions by using concept of conic domain. Furthermore, we find non-sharp estimates on the first two Taylor-Maclaurin coefficients $ left vert a_{2}right vert $ and $left vert a_{3}right vert $ for functions in these new subclasses. We consider various corollaries and consequen...

Maximal Functions Associated to Filtrations

Let T be a bounded linear, or sublinear, operator from L p (Y) to L q (X). To any sequence of subsets Y j of Y is associated a maximal operator T f(x) = sup j jT (f Yj)(x)j. Under the hypotheses that q > p and the sets Y j are nested, we prove that T is also bounded. Classical theorems of Menshov and Zygmund are obtained as corollaries. Multilinear generalizations of this theorem are also estab...

Cylindrical Estimates for Hypersurfaces Moving by Convex Curvature Functions

Convexity estimates for hypersurfaces moving by convex curvature functions

We consider the evolution of compact hypersurfaces by fully non-linear, parabolic curvature ows for which the normal speed is given by a smooth, convex, degree one homogeneous function of the principal curvatures. We prove that solution hypersurfaces on which the speed is initially positive become weakly convex at a singularity of the ow. The result extends the convexity estimate [HS99b] of Hui...

Existence of positive solutions for a Schrödinger-Poisson system with bounded potential and weighted functions in R3$\mathbb{R}^{3}$

where V (x), a(x) and b(x) are positive and bounded in R, K(x) ∈ L(R) ∪ L∞(R) and K(x) ≥  in R. We will prove the existence of a positive solution (u,φ) ∈ W ,(R) × D,(R) for λ ∈R and  < q <m < ∗, where ∗ =  is the critical exponent for the Sobolev embedding in dimension . The assumption ‘ < q <m < ’ implies that the nonlinear term f (x,u) = a(x)|u|m–u + λb(x)|u|q–u in (.)...