Reflexivity of Inductive Limits

An inductive locally convex limit of reflexive topological spaces is reflexive iff it is almost regular.     

Transmission problems and spectral theory for singular integral operators on Lipschitz domains

We prove the well-posedness of the transmission problem for the Laplacian across a Lipschitz interface, with optimal non-tangential maximal function estimates, for data in Lebesgue and Hardy spaces on the boundary. As a corollary, we show that the spectral radius of the (adjoint) harmonic double layer potential K∗ in is less than , whenever is a bounded convex domain and 1<p?2.     

Small into isomorphisms on uniformly smooth spaces

Let X be a uniformly smooth infinite dimensional Banach space, and (Ω,Σ,μ) be a σ-finite measure space. Suppose that T:X→L∞(Ω,Σ,μ) satisfies

(1−ε)‖x‖?‖Tx‖?‖x‖,∀x∈X,     

Algebraic independence of the values of Mahler functions associated with a certain continued fraction expansion

It is proved that the function , which can be expressed as a certain continued fraction, takes algebraically independent values at any distinct nonzero algebraic numbers inside the unit circle if the sequence {R_k}_k?0 is the generalized Fibonacci numbers.     

Global Solutions of an Obstacle-Problem-Like Equation with Two Phases

Concerning the obstacle-problem-like equation , where ₊ > 0 and _– > 0, we give a complete characterization of all global two-phase solutions with quadratic growth both at 0 and infinity.     

关于高维蝴蝶定理

利用距离几何方法将古典的蝴蝶定理推广到n维欧氏空间一般二次超曲面情形,同时也得到高维蝴蝶定理的逆定理.     

COEFFICIENT MULTIPLIERS ON MIXED NORM SPACES

§1　IntroductionSuppose thatf is analytic in the open unit disc D in the complex plane.We defineMp(r,f) =12π∫2π0 | f(reiθ) | pdθ1 / p,0

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Maximal invariant subspaces for

We find the maximal invariant subspaces for on -valued Bergman-type spaces.

     

Bicircular projections and characterization of Hilbert spaces

We prove that every JB* triple with rank one bicircular projection is a direct sum of two ideals, one of which is isometrically isomorphic to a Hilbert space.

     

Uncorrelatedness and orthogonality for vector-valued processes

For a square integrable vector-valued process on the Loeb product space, it is shown that vector orthogonality is almost equivalent to componentwise scalar orthogonality. Various characterizations of almost sure uncorrelatedness for are presented. The process is also related to multilinear forms on the target Hilbert space. Finally, a general structure result for involving the biorthogonal representation for the conditional expectation of with respect to the usual product -algebra is presented.