Let T be the singular integral operator, a well-known result of Coifman, Rochberg and Weiss [6] which states that the commutator [b,T ] = T (b f )− bT f (where b ∈ BMO) is bounded on Lp(Rn)(1 < p < ∞). Chanillo [1] proves a similar result when T is replaced by the fractional integral operator. In [9,11], these results on the Triebel–Lizorkin spaces and the case b∈Lipβ (where Lipβ is the homogen...

It is well known that the Hankel transform possesses neither a shift-modulation nor a convolution-multiplication rule, both of which have found many uses when used with other integral transforms. In this paper, the generalized shift operator, as defined by Levitan, is applied to the Hankel transform. It is shown that under this generalized definition of shift, both convolution and shift theorem...

This paper presents an analytic formulation for anti-aliased sampling of 2D polygons and 3D polyhedra. Our framework allows the exact evaluation of the convolution integral with a linear function defined on the polytopes. The filter is a spherically symmetric polynomial of any order, supporting approximations to refined variants such as the Mitchell-Netravali filter family. This enables high-qu...

The X s,b spaces, as used by Beals, Bourgain, Kenig-Ponce-Vega, Klainerman-Machedon and others, are fundamental tools to study the low-regularity behaviour of non-linear dispersive equations. It is of particular interest to obtain bilinear or multilinear estimates involving these spaces. By Plancherel's theorem and duality, these estimates reduce to estimating a weighted convolution integral in...

Graph neural networks (GNNs) extends the functionality of traditional to graph-structured data. Similar CNNs, an optimized design graph convolution and pooling is key success. Borrowing ideas from physics, we propose a path integral based (PAN) for classification regression tasks on graphs. Specifically, consider operation that involves every linking message sender receiver with learnable weigh...

Abstract Vortex cores in fluid mechanics are easy to visualize, yet difficult detect numerically. Precise knowledge of these allows dynamics researchers study complex flow structures and allow for a better understanding the turbulence transition process development evolution instabilities, name but few relevant areas. Various approaches such as Q, delta, swirling strength criterion have been pr...