Hausdorff operator in Lebesgue spaces

On Gromov-hausdorff Convergence for Operator Metric Spaces

We introduce an analogue for Lip-normed operator systems of the second author’s order-unit quantum Gromov-Hausdorff distance and prove that it is equal to the first author’s complete distance. This enables us to consolidate the basic theory of what might be called operator Gromov-Hausdorff convergence. In particular we establish a completeness theorem and deduce continuity in quantum tori, Bere...

Decomposition of Lebesgue Spaces

Norm inequalities for the conjugate operator in two-weighted Lebesgue spaces

* Correspondence: ksrim@sogang. ac.kr Department of Mathematics, Sogang University, Seoul 121-742, Korea Abstract In this article, first, we prove that weighted-norm inequalities for the M-harmonic conjugate operator on the unit sphere whenever the pair (u, v) of weights satisfies the Ap-condition, and uds, vds are doubling measures, where ds is the rotationinvariant positive Borel measure on t...

The Sampling Theorem in Variable Lebesgue Spaces

hold. The facts above are well-known as the classical Shannon sampling theorem initially proved by Ogura [10]. Ashino and Mandai [1] generalized the sampling theorem in Lebesgue spaces L0(R) for 1 < p0 < ∞. Their generalized sampling theorem is the following. Theorem 1.1 ([1]). Let r > 0 and 1 < p0 < ∞. Then for all f ∈ L 0(R) with supp f̂ ⊂ [−rπ, rπ], we have the norm inequality C p r ‖f‖Lp0(Rn...

Modal compact Hausdorff spaces

We introduce modal compact Hausdorff spaces as generalizations of modal spaces, and show these are coalgebras for the Vietoris functor on compact Hausdorff spaces. Modal compact regular frames and modal de Vries algebras are introduced as algebraic counterparts of modal compact Hausdorff spaces, and dualities are given for the categories involved. These extend the familiar Isbell and de Vries d...