In this article, the spectral theory is considered, we study families and their correspondence to operators on reflexive Banach spaces; assume A a well-bounded operator Lebesgue spaces then scalar type operator. The main goals are obtain characterization of in terms associated family topology dual pairing construct continuous functional calculus for space.

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...

In this paper, we prove the boundedness of the multilinear commutator related to the singular integral operator in Morrey and Morrey-Herz spaces on homogeneous spaces. 2000 Mathematics Subject Classification: 42B20, 42B25. 1. Preliminaries Sawano and Tanka(see [13]) introduced the Morrey spaces on the non-homogeneous spaces and proved the boundedness of Hardy-Littlewood maximal operators, Calde...

The discrete Morrey space m_(u,p) is a generalization of the p-summable sequence l^p. We have known that normed space, but equipped with usual norm not an inner product for p equal to 2. In this paper, we shall show actually contained in space. That means relationship between standard on and studied.

The unfolding of a vector field exhibiting a degenerate homoclinic orbit of inclination-flip type is studied. The linear part of the unperturbed system possesses a resonance but the coefficient of the corresponding monomial vanishes. We show that for an open set in the parameter space, the system possesses a suspended cubic Hénon-like map. As a consequence, strange attractors with entropy close...

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...

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...