We prove a weighted norm inequality for the maximal Bochner-Riesz operator and the associated square-function. This yields new L(R) bounds on classes of radial Fourier multipliers for p ≥ 2 + 4/d with d ≥ 2, as well as space-time regularity results for the wave and Schrödinger equations.

In this paper we construct infinitely many selfadjoint solutions of the control algebraic Riccati equation using invariant subspaces of the associated Hamiltonian. We do this under the assumption that the system operator is normal and has compact inverse, and that the Hamiltonian possesses a Riesz basis of invariant subspaces.

We prove weighted norm inequalities for fractional powers of elliptic operators together with their commutators with BMO functions, encompassing what is known for the classical Riesz potentials and elliptic operators with Gaussian domination by the classical heat operator. The method relies upon a good-λ method that does not use any size or smoothness estimates for the kernels.

Let T be a singular nonintegral operator; that is, it does not have an integral representation by a kernel with size estimates, even rough. In this paper, we consider the boundedness of commutators with T and Lipschitz functions. Applications include spectral multipliers of self-adjoint, positive operators, Riesz transforms of second-order divergence form operators, and fractional power of elli...

Spectral problem for the Dirac operator with regular but not strongly boundary conditions and complex-valued potential summable over a finite interval is considered. The purpose of this paper to find under which root function system forms usual Riesz basis rather than parentheses.

In this paper, we consider evolution equations in the abstract Hilbert space under special conditions imposed on operator at right-hand side of equation. We establish method that allows us to formulate existence and uniqueness theorem find a solution form series root vectors side. fractional differential various kinds as an application. Such operators Riemann-Liouville operator, Riesz potential...

We introduce the class of quasi-square-2-isometric operators on a complex separable Hilbert space. This extends 2-isometric due to Agler and Stankus. An operator T is said be if T*5T5 ? 2T*3T3 + T*T = 0. In this paper, we give matrix representation in order obtain spectral properties operator. particular, show that function continuous all operators. Under hypothesis ?(T)?(??(T)) ?, also prove E...

We employ an operator theoretic setting established in [2]. Under Condition 2.1 below, a self-adjoint (actually quasi-uniformly positive [7]) operator A in the Krein space L2,r(−1, 1)⊕C 2 ∆ is associated with the eigenvalue problem (1.1), (1.2). Here ∆ is a 2 × 2 nonsingular Hermitean matrix which is determined by M and N; see Section 2 for details. We remark that the topology of this Krein spa...

The classical theorems of Riesz [l] on compact operators have been extended by Leray [2] and Williamson [3] to the context of topological linear spaces. Ringrose [4] has shown that if an operator on such a space is compact, the square of its adjoint is also compact, where the topology on the dual space is that of uniform convergence on bounded sets. Thus if an operator is continuous and some po...