This paper is devoted to $$L^2$$ estimates for trilinear oscillatory integrals of convolution type on $${\mathbb {R}}^2$$ . The phases in the factors include smooth functions and polynomials. We shall establish sharp decay with phases, then give uniform these polynomial phases.

We study perturbations of type B r of Dirichlet operators (L 0 ; D(L 0)) associated with Dirichlet forms of type E 0 (u; v) = 1=2

Let X be a metric space with doubling measure, L be a nonnegative selfadjoint operator in L2(X ) satisfying the Davies-Gaffney estimate, ω be a concave function on (0,∞) of strictly lower type pω ∈ (0, 1] and ρ(t) = t/ω(t) for all t ∈ (0,∞). The authors introduce the Orlicz-Hardy space Hω,L(X ) via the Lusin area function associated to the heat semigroup, and the BMO-type space BMOρ,L(X ). The ...

Practical solid modeling systems are plagued by numerical problems that arise from using floating-point arithmetic. For example, polyhedral solids are often represented by a combination of geometric and combinatorial information. The geometric information may consist of explicit plane equations, with floatingpoint coefficients; the combinatorial information may consist of face, edge, and vertex...

Let p be a prime greater than three. In the p–local stable homotopy groups of spheres, R L Cohen constructed the infinite –element n 1 2 2pnC1 2pnC2p 5.S/ of order p . In the stable homotopy group 2pnC1 2pnC2p2 3.V .1// of the Smith– Toda spectrum V .1/ , X Liu constructed an essential element $k for k 3 . Let ˇ s D j0j1ˇ s 2 ŒV .1/;S 2sp2 2s 2p denote the Spanier–Whitehead dual of the generat...

We present two ways in which the model L(R) is canonical assuming the existence of large cardinals. We show that the theory of this model, with ordinal parameters, cannot be changed by small forcing; we show further that a set of ordinals in V cannot be added to L(R) by small forcing. The large cardinal needed corresponds to the consistency strength of ADL(R); roughly ω Woodin cardinals.

In [3, 4] Törnquist and Weiss proved many natural Σ2 definable counterparts of classical equivalences to the Continuum Hypothesis (CH). These become equivalent to “all reals are constructible”. Following this scheme, we proved definable counterparts for some algebraic equivalent form of CH. More specifically we obtained a Σ2 version of a result about avoidable polynomials proven by Schmerl [2]....

The paper studies language equations of the type X ⋄ L = R and L ⋄ Y = R, where L and R are given languages and ⋄ is an invertible binary word(language) operation. For most of the considered insertion and deletion operations, the existence of both a solution and a singleton solution to these equations proves to be decidable for given regular L and R. In case L is a context-free language and R i...

We establish $L^{p_1}\times\cdots\times L^{p_k}\to L^r$ and $\ell^{p_1}\times\cdots\times \ell^{p_k}\to \ell^r$ type bounds for multilinear maximal operators associated to averages over isometric copies of a given non-degenerate $k$-simplex in both the continuous discrete settings. These provide natural extensions $L^p\to L^p$ $\ell^p\to \ell^p$ Stein's spherical operator operator, with each th...

In bilateria, positioning and looping of visceral organs requires proper left-right (L/R) asymmetry establishment. Recent work in Drosophila has identified a novel situs inversus gene encoding the unconventional type ID myosin (MyoID). In myoID mutant flies, the L/R axis is inverted, causing reversed looping of organs, such as the gut, spermiduct and genitalia. We have previously shown that Myo...