This paper concerns the continuous-time, mean-variance portfolio selection problem in a complete market with random interest rate, appreciation rates, and volatility coefficients. The problem is tackled using the results of stochastic linear-quadratic (LQ) optimal control and backward stochastic differential equations (BSDEs), two theories that have been extensively studied and developed in rec...

In this article, we consider an analogue of Kenig and Stein's bilinear fractional integral operator on the Heisenberg group Hn. We completely characterize exponents α,β γ such that is bounded from Lp(Hn,|x|αp)×Lq(Hn,|x|βq) to Lr(Hn,|x|−γr). Also, analogous sharp results are obtained Euclidean space.

For fast ε-similarity search, various index structures have been proposed. Yi et al. proposed a concept multimodality support and suggested inequalities by which εsimilarity search by L1, L2 and L∞ norm can be realized. We proposed an extended inequality which allows us to realize ε-similarity search by arbitrary Lp norm using an index based on Lq norm. In these investigations a search radius o...

Consider the partition function S μ( ) associated in the theory of Rényi dimension to a finite Borel measure μ on Euclidean d-space. This partition function S μ( ) is the sum of the q-th powers of the measure applied to a partition of d-space into d-cubes of width . We further Guérin’s investigation of the relation between this partition function and the Lebesgue Lp norm (Lq norm) of the convol...

We study some structural aspects of the subspaces of the non-commutative (Haagerup) Lp-spaces associated with a general (non necessarily semi-finite) von Neumann algebra a. If a subspace X of Lp(a) contains uniformly the spaces lnp , n ≥ 1, it contains an almost isometric, almost 1-complemented copy of lp. If X contains uniformly the finite dimensional Schatten classes S p , it contains their l...

We prove that a two-variable p-adic lq-function has the series expansion lp,q s, t, χ 2 q/ 2 F ∑F a 1, p,a 1 −1 a χ a qa/〈a pt〉 ∑∞ m 0 −s m F/〈a pt〉 mE∗ m,qF which interpolates the values lp,q −n, t, χ E∗ n,χn,q pt − pχn p 2 q/ 2 qp E∗ n,χn,q t , whenever n is a nonpositive integer. The proof of this original construction is due to Kubota and Leopoldt in 1964, although the method given in this ...

Two–sided estimates of Schatten–von Neumann norms for weighted Volterra integral operators are established. Analogous problems for some potential-type operators defined on R are solved. Let H be a separable Hilbert space and let σ∞(H) be the class of all compact operators T : H → H, which forms an ideal in the normed algebra B of all bounded linear operators onH. To construct a Schattenvon Neum...

In this paper we deal with a definition of Lp-Fourier transform on locally compact groups. Recall that, for locally compact abelian groups, the Hausdorff-Young inequality reads: Let 1 < p < 2 and q = p/(p − 1). If g ∈ L1(G) ∩ Lp(G), then ĝ ∈ Lq(Ĝ), with ‖ĝ‖q ≤ ‖g‖p. The inequality allows to extend the Fourier transform to a continuous operator Fp : Lp → Lq by continuity. It was generalized to t...

Consider estimating the mean vector from data Nn( ; I) with lq norm loss, q 1, when is known to lie in an n-dimensional lp ball, p 2 (0;1). For large n, the ratio of minimax linear risk to minimax risk can be arbitrarily large if p < q. Obvious exceptions aside, the limiting ratio equals 1 only if p = q = 2. Our arguments are mostly indirect, involving a reduction to a univariate Bayes minimax ...