In this paper, we obtain a refinement of the Young theorem. The Young theorem tells us that the Fourier transform F sends the L functions to the Lp functions, if 1 ≤ p ≤ 2. This theorem has a refinement. For example, F : L → B ∞1, where B pq is the Besov space. In this present paper we shall consider the more refined version of this theorem by using the amalgams and the Besov spaces.

This paper gives an abstract version of de Finetti’s theorem that characterizes mixing measureswith Lp densities. The general setting is reviewed; after the theorem is proved, it is specializedto coin tossing and to exponential random variables. Laplace transforms of bounded densities arecharacterized, and inversion formulas are discussed.

In this paper, we study weighted Lp?q minimization model which comprises non-smooth, nonconvex and non-Lipschitz quasi-norm Lp(0 < p ? 1) Lq(1 q 2) for recovering sparse signals. Based on the restricted isometry property (RIP) condition, obtain exact signal recovery result. We also theoretical bound when measurements are depraved by noises.

In this work we investigate n-widths of multiplier operators Λ∗ and Λ, defined for functions on the complex sphere Ωd ℂd, associated with sequences multipliers type {λm,n∗}m,n∈N, λm,n∗=λ(m+n) {λm,n}m,n∈N, λm,n=λ(max{m,n}), respectively, a bounded function λ [0,∞). If Λ are from Lp(Ωd) into Lq(Ωd), 1≤p,q≤∞, Up is closed unit ball Lp(Ωd), study lower upper estimates Kolmogorov, linear, Gelfand Be...

It is well known that for P and Q lattice polytopes, the Ehrhart polynomial of P×Q satisfies LP×Q(t) = LP (t)LQ(t). We show that there is a similar multiplicative relationship between the Ehrhart series for P , for Q, and for the free sum P ⊕ Q that holds when P is reflexive and Q contains 0 in its interior. Let P be a lattice polytope of dimension d, i.e. a convex polytope in R whose vertices ...

We give a negative solution to the problem of the Lp-maximal regularity on various classes of Banach spaces including Lq-spaces with 1 < q / = 2 < +∞. Mathematics Subject Classification (1991):47D06, 46B03, 46B52, 46C15

We present an isoperimetric inequality for a nonlinear generalization of the first twisted Dirichlet eigenvalue. Let λ(Ω) be the set functional defined by λ(Ω) = inf { ‖∇v‖Lp(Ω) ‖v‖Lq(Ω) , v ∈W }

and Applied Analysis 3 for any fixed T > 0. Then v,H can be extended beyond T > 0 if one of the following conditions is satisfied: 1 u ∈ C ( 0, T ;Ln/3 ) , 1.11 2 u ∈ L 0, T ;L with 2 p n q 3, n 3 < q ≤ n, 1.12 3 ∇u ∈ C ( 0, T ;Ln/4 ) , 1.13 4 ∇u ∈ L 0, T ;L with 2 p n q 4 with n 4 < q ≤ n 2 . 1.14 Remark 1.5. If we delete the harmless lower order terms ∂tu − Δu and ∂tB − ΔB in 1.1 and 1.2 , th...

In this article, we begin with Riesz potential. We then discuss some properties of the Finally a relation Potential fractional maximal function in sense that can be controlled by potential and maps space Lp to Lq whenever does.