In this paper we will prove several weighted estimates for bilinear fractional integral operators and their commutators with BMO functions. We also prove maximal function control theorem for these operators, that is, we prove the weighted Lp norm is bounded by the weighted Lp norm of a natural maximal operator when the weight belongs to A∞. As a corollary we are able to obtain new weighted esti...

The compact city is becoming a prevailing paradigm in the world to control urban sprawl and achieve a pattern of sustainable urban development. However, discussions of the area's overcrowded neighborhoods, its health problems, and the destruction of its green areas have inspired self-examination with respect to the compact city paradigm. High population density attracts even more residents and ...

We calculate partition functions for lens spaces Lp,q up to p = 8 and for genus 1 and 2 handlebodies H1, H2 in the Turaev-Viro framework. These can be interpreted as transition amplitudes in 3D quantum gravity. In the case of lens spaces Lp,q these are vacuum-to-vacuum amplitudes Ø → Ø, whereas for the 1and 2-handlebodies H1, H2 they represent genuinely topological transition amplitudes Ø → T 2...

We study dispersive mixed-order systems of pseudodifferential operators in the setting of Lp-Sobolev spaces. Under the weak condition of quasihyperbolicity, these operators generate a semigroup in the space of tempered distributions. However, if the basic space is a tuple of Lp-Sobolev spaces, a strongly continuous semigroup is in many cases only generated if p = 2 or n = 1. The results are app...

We investigate the structure of shift-invariant spaces generated by a finite number of compactly supported functions in Lp(R) (1 ≤ p ≤ ∞). Based on a study of linear independence of the shifts of the generators, we characterize such shift-invariant spaces in terms of the semi-convolutions of the generators with sequences on Z. Moreover, we show that such a shiftinvariant space provides Lp-appro...

We construct classes of von Neumann algebra modules by considering “column sums” of noncommutative Lp spaces. Our abstract characterization is based on an Lp/2-valued inner product, thereby generalizing Hilbert C*-modules and representations on Hilbert space. While the (single) representation theory is similar to the L2 case, the concept of Lp bimodule (p 6= 2) turns out to be nearly trivial.