We give characterizations of radial Fourier multipliers as acting on radial L functions, 1 < p < 2d/(d + 1), in terms of Lebesgue space norms for Fourier localized pieces of the convolution kernel. This is a special case of corresponding results for general Hankel multipliers. Besides L −L bounds we also characterize weak type inequalities and intermediate inequalities involving Lorentz spaces....

In this paper we introduce and investigate a Henstock-Kurzweil-type integral for Riesz-space-valued functions defined on (not necessarily bounded) subintervals of the extended real line. We prove some basic properties, among them the fact that our integral contains under suitable hypothesis the generalized Riemann integral and that every simple function which vanishes outside of a set of finite...

Abstract Uniqueness of Leray solutions the 3D Navier-Stokes equations is a challenging open problem. In this article we will study problem for stationary in whole space R 3 . Under some additional hypotheses, stated terms Lebesgue and Morrey spaces, show that trivial solution U ? = 0 unique solution. This type results are known as Liouville theorems.

It is proved that for any d ≥ 3, there exists a norm ‖ · ‖ and two points a, b in Rd such that the boundary of the Leibniz half-space H(a, b) = {x ∈ Rd : ‖x − a‖ ≤ ‖x − b‖} has non-zero Lebesgue measure. When d = 2, it is known that the boundary must have zero Lebesgue measure.

Abstract In this paper, we study the Sobolev regularity of solutions to nonlinear second order elliptic equations with super-linear first-order terms on Riemannian manifolds, complemented Neumann boundary conditions, when source term equation belongs a Lebesgue space, under various integrability regimes. Our method is based an integral refinement Bochner identity, and leads “semilinear Calderón...

Resource-bounded measure is a generalization of classical Lebesgue measure that is useful in computational complexity. The central parameter of resource-bounded measure is the resource bound ∆, which is a class of functions. When ∆ is unrestricted, i.e., contains all functions with the specified domains and codomains, resource-bounded measure coincides with classical Lebesgue measure. On the ot...

Space, as we typically represent it in mathematics and physics, is composed of dimensionless, indivisible points. But philosophers have for a long time doubted whether there are any point-sized regions of space. On an alternative, region-based approach to space, extended regions together with the relations of parthood and contact are taken as primitive; points are represented as mathematical ab...

The influence theorem for product measures on the discrete space {0, 1}N may be extended to probability measures with the property of monotonicity (which is equivalent to ‘strong positive-association’). Corresponding results are valid for probability measures on the cube [0, 1]N that are absolutely continuous with respect to Lebesgue measure. These results lead to a sharp-threshold theorem for ...

the purpose of the present work is to establish a one-to-one correspondence between the family of interval type-2 fuzzy reflexive/tolerance approximation spaces and the family of interval type-2 fuzzy closure spaces.

Let H be a complex Hilbert space. Denote by B(H)+ the set of all positive bounded linear operators on H. A bijective map φ : B(H)+ → B(H)+ is said to preserve Lebesgue decompositions in both directions if for any quadruple A,B,C,D of positive operators, B = C +D is an A-Lebesgue decomposition of B if and only if φ(B) = φ(C)+φ(D) is a φ(A)-Lebesgue decomposition of φ(B). It is proved that every ...