Lp–Lq decay estimates of solutions to Cauchy problems of linear thermoelastic systems with second sound in three spatial variables are studied. By carefully analysis of the different effects of higher, middle and lower frequencies in phase space, the asymptotic behaviour of characteristic roots of coefficient matrices is obtained. Then, with the help of the information on characteristic roots a...

Let G be a locally compact abelian group with dual group Ĝ. The Hausdorff–Young theorem states that if f ∈ Lp(G), where 1 ≤ p ≤ 2, then its Fourier transform Fp(f) belongs to Lq(Ĝ) (where 1 p + 1 q = 1) and ||Fp(f)||q ≤ ||f ||p. Kunze and Terp extended this to unimodular and locally compact groups, respectively. We further generalize this result to an arbitrary locally compact quantum group G b...

In this paper, we deal with the biharmonic heat equation gradient non-linearity. Under suitable condition of initial datum, show that global unique existence mild solution. The main technique in paper is to use Banach?s fixed point theorem combination Lp-Lq evaluation operator.

For the spaces φ(X0, X1)p0,p1 , which generalize the spaces of means introduced by Lions and Peetre to the case of functional parameters, necessary and sufficient conditions are found for embedding when all parameters (the function φ and the numbers 1 ≤ p0, p1 ≤ ∞) vary. The proof involves a description of generalized Lions–Peetre spaces in terms of orbits and co-orbits of von Neumann–Schatten ...

Let I = [a, b] ⊂ R, let 1 < q ≤ p <∞, let u and v be positive functions with u ∈ Lp′(I), v ∈ Lq(I) and let T : Lp(I) → Lq(I) be the Hardy-type operator given by

Let 1 p 1 and W : R ! (0;1) be continuous. Does W admit a Jackson Theorem in Lp? That is, does there exist a sequence f ng 1 n=1 of positive numbers with limit 0 such that inf deg(P ) n k (f P )W kLp(R) n k f W kLp(R) for all absolutely continuous f with k f 0W kLp(R) …nite? We show that such a theorem is true i¤ lim x!1 W 1 Lq [0;x] kWkLp[x;1) = 0; where q is the conjugate parameter of p. In a...

Given two Banach spaces X and Y , we write L(X, Y ) for the space of all continuous linear operators from X to Y . A linear subspace J of L(X, Y ) is said to be an ideal if ATB ∈ J whenever A ∈ L(Y ), T ∈ J , and B ∈ L(X). It is known (see, e.g., Caradus:74 [CPY74]) that the only norm closed ideal in L(lp), 1 6 p < ∞ is the ideal of compact operators. The structure of closed ideals in L(lp ⊕ lq...