The generalized Beurling–Ahlfors operator S on L(R; Λ), where Λ := Λ(R) is the exterior algebra with its natural Hilbert space norm, satisfies the estimate ‖S‖L (Lp(Rn;Λ)) ≤ (n/2 + 1)(p ∗ − 1), p∗ := max{p, p′}. This improves on earlier results in all dimensions n ≥ 3. The proof is based on the heat extension and relies at the bottom on Burkholder’s sharp inequality for martingale transforms.

Some reverses of the continuous triangle inequality for Bochner integral of vectorvalued functions in Hilbert spaces are given. Applications for complex-valued functions are provided as well.

A singular value inequality due to Bhatia and Kittaneh says that if A and B are compact operators on a complex separable Hilbert space such that A is self-adjoint, B 0, and A B; then sj(A) sj(B B) for j = 1; 2; :::We give an equivalent inequality, which states that if A;B; and C are compact operators such that A B B C 0; then sj(B) sj(A C) for j = 1; 2; :::Moreover, we give a sharper inequality...

This paper develops several aspects of shift-invariant spaces on locally compact abelian groups. For a second countable locally compact abelian group G we prove a useful Hilbert space isomorphism, introduce range functions and give a characterization of shift-invariant subspaces of L 2 (G) in terms of range functions. Utilizing these functions, we generalize characterizations of frames and Ries...

We consider stochastic equations in Hilbert spaces with singular drift in the framework of [7]. We prove a Harnack inequality (in the sense of [18]) for its transition semigroup and exploit its consequences. Supported in part by “Equazioni di Kolmogorov” from the Italian “Ministero della Ricerca Scientifica e Tecnologica” Supported by the DFG through SFB-701 and IRTG 1132, by nsf-grant 0603742 ...

Let T be a continuous linear map V → V for a (separable) Hilbert space V . Its spectrum σ(T ) is a compact subset of R, so is certainly contained in some finite interval [a, b]. As usual, for a self-adjoint continuous operator S on V , write S ≥ 0 when 〈Sv, v〉 ≥ 0 for all v ∈ V . For self-adjoint S, T , write S ≤ T when T − S ≥ 0. At the outset, with a ≤ −|T |op and b ≥ |T |op, we have, 〈a · v,...

This online supplement provides additional material to accompany “Framing Contingencies” by Ahn and Ergin. We characterize monotonicity, subadditivity, and superadditivity of the support function. We connect the case where the available partitions constitute a filtration and the case where all partitions are available. We define a local notion of transparency relative to a description of the st...

The study of design and formation of urban space focuses on interaction of human and environment. This is an attractive subject that considers as interdisciplinary debates. Thinkers of urban studies pay attention to this matter empirically and theoretically in order to provide a desirable space for human being. This research is based on the theories of urban studies and urban sociology and so o...