Lq-THEORY OF A SINGULAR “WINDING” INTEGRAL OPERATOR ARISING FROM FLUID DYNAMICS

Exact and semiclassical approach to a class of singular integral operators arising in fluid mechanics and quantum field theory

A class of singular integral operators, encompassing two physically relevant cases arising in perturbative QCD and in classical fluid dynamics, is presented and analyzed. It is shown that three special values of the parameters allow for an exact eigenfunction expansion; these can be associated to Riemannian symmetric spaces of rank one with positive, negative or vanishing curvature. For all oth...

$L_{p;r} $ spaces: Cauchy Singular Integral, Hardy Classes and Riemann-Hilbert Problem in this Framework

In the present work the space  $L_{p;r} $ which is continuously embedded into $L_{p} $  is introduced. The corresponding Hardy spaces of analytic functions are defined as well. Some properties of the functions from these spaces are studied. The analogs of some results in the classical theory of Hardy spaces are proved for the new spaces. It is shown that the Cauchy singular integral operator is...

A Sharp Maximal Function Estimate for Vector-Valued Multilinear Singular Integral Operator

We establish a sharp maximal function estimate for some vector-valued multilinear singular integral operators. As an application, we obtain the $(L^p, L^q)$-norm inequality for vector-valued multilinear operators.

Numerical Solution of Singular IVPs of Lane-Emden Type Using Integral Operator and Radial Basis Functions

Positivity and topology in lattice gauge theory

With certain smoothness assumptions, continuum Yang-Mills field configurations in four dimensional spacetime can be classified by a topological winding number [1]. This realization has played a major role in our understanding of the importance of nonperturbative phenomena in the SU(3) gauge theory of the strong interactions [2]. This winding number is uniquely defined for smooth fields; however...