We introduce a condition on accretive matrix functions, called p -ellipticity, and discuss its applications to the L^p theory of elliptic PDEs with complex coefficients. Our examples are: (i) generalized convexity of power functions (Bellman functions), (ii) dimension-free bilinear embeddings, (iii) L^p -contractivity of semigroups, and (iv) holomorphic functional calculus. Recent work by Dindos and Pipher established close ties between p -ellipticity and (v) regularity theory of elliptic PDEs with complex coefficients. The p -ellipticity condition arises from studying uniform positivity of a quadratic form associated with the matrix in question on the one hand, and the Hessian of a power function on the other. Our results regarding contractivity extend earlier theorems by Cialdea and Maz’ya.

We prove that every generator of a symmetric contraction semigroup on a $\sigma$-finite measure space admits, for $1

In a previous paper the authors developed a H 1 −BM O theory for unbounded metric measure spaces (M, ρ, µ) of infinite measure that are locally doubling and satisfy two geometric properties, called "approximate midpoint" property and "isoperimetric" property. In this paper we develop a similar theory for spaces of finite measure. We prove that all the results that hold in the infinite measure case have their counterparts in the finite measure case. Finally, we show that the theory applies to a class of unbounded, complete Riemannian manifolds of finite measure and to a class of metric measure spaces of the form (R d , ρϕ, µϕ), where dµϕ = e −ϕ dx and ρϕ is the Riemannian metric corresponding to the length element ds 2 = (1+|∇ϕ|) 2 ( dx 2 1 +· · ·+ dx 2 d ). This generalizes previous work of the last two authors for the Gauss space.2000 Mathematics Subject Classification. 42B20, 42B30, 46B70, 58C99 .

MultiAnalyte immunoassays are often required to diagnose a pathologic condition. Here, we show how resistive-pulse sensing and multiple artificial pores can be integrated together on a single chip to detect different antigens rapidly and simultaneously. We use multiple pores on a single chip to detect the size change of latex colloids upon specific antigen-antibody binding on the colloid surface. As a proof-of-principle, we demonstrate our ability to detect simultaneously human G-CSF and GM-CSF antigens on a single chip. Our novel technique is a scalable technology that can lead to the sensing of at least N2 antigens simultaneously with an N N array of pores on a single chip.

Abstract. By using an explicit Bellman function, we prove a bilinear embedding theorem for the Laplacian associated with a weighted Riemannian manifold (M, µϕ) having the Bakry-Emery curvature bounded from below. The embedding, acting on the Cartesian product of L p (M, µϕ) and L q (T * M, µϕ),