We prove that the Banach spaces (⊕n=1`p )`q , which are isomorphic to the Besov spaces on [0, 1], have greedy bases, whenever 1 ≤ p ≤ ∞ and 1 < q < ∞. Furthermore, the Banach spaces (⊕n=1`p )`1 , with 1 < p ≤ ∞, and (⊕n=1`p )c0 , with 1 ≤ p < ∞ do not have a greedy bases. We prove as well that the space (⊕n=1`p )`q has a 1-greedy basis if and only if 1 ≤ p = q ≤ ∞.

We consider the dilation property of the modulation spaces M. Let Dλ : f(t) 7→ f(λt) be the dilation operator, and we consider the behavior of the operator norm ‖Dλ‖Mp,q→Mp,q with respect to λ. Our result determines the best order for it, and as an application, we establish the optimality of the inclusion relation between the modulation spaces and Besov space, which was proved by Toft [9].

In this article, we consider the Cauchy problem for dispersive equations in α-Modulation spaces. For this purpose, we find a method for estimating uk in α-modulation spaces when k is not an integer, and develop a Strichartz estimate in M p,q which is based on semigroup estimates. In the local case, we that the domain of p is independent of α, which is also the case in the Modulation spaces and ...

In this paper, we comment on the complexity of the invariant subspaces (under the bilateral Dirichlet shift f → ζf ) of the harmonic Dirichlet space D. Using the sampling theory of Seip and some work on invariant subspaces of Bergman spaces, we will give examples of invariant subspaces F ⊂ D with dim(F /ζF ) = n, n ∈ N ∪ {∞}. We will also generalize this to the Dirichlet classes Dα, 0 < α < ∞, ...

ABSTRACT. It is known that the energy of a weak solution to the Euler equation is conserved if it is slightly more regular than the Besov space B 3,∞. When the singular set of the solution is (or belongs to) a smooth manifold, we derive various L-space regularity criteria dimensionally equivalent to the critical one. In particular, if the singular set is a hypersurface the energy of u is conser...

In this paper, we first generalize the classical results on Cauchy problem for positive symmetric quasilinear systems to more general Besov space. Through this generalization, we obtain the local well-posedness with initial data in the space B d 2 +1 2,1 (R ) which has critical regularity index. We then apply these results to give an explicit characterization on the Isentropic approximation for...

We consider parameter-elliptic boundary value problems and uniform a priori estimates in Lp-Sobolev spaces of Bessel potential and Besov type. The problems considered are systems of uniform order and mixed-order systems (Douglis-Nirenberg systems). It is shown that compatibility conditions on the data are necessary for such estimates to hold. In particular, we consider the realization of the bo...

This paper studies the Cauchy problem for the nonlinear fractional power dissipative equation ut + (−△) u = F (u) for initial data in the Lebesgue space L(R) with r ≥ rd , nb/(2α− d) or the homogeneous Besov space Ḃ p,∞(R ) with σ = (2α − d)/b − n/p and 1 ≤ p ≤ ∞, where α > 0, F (u) = f(u) or Q(D)f(u) with Q(D) being a homogeneous pseudo-differential operator of order d ∈ [0, 2α) and f(u) is a ...

We consider an Orlicz space based cohomology for metric (measured) spaces with bounded geometry. We prove the quasi-isometry invariance for a general Young function. In the hyperbolic case, we prove that the degree one cohomology can be identified with an Orlicz-Besov function space on the boundary at infinity. We give some applications to the large scale geometry of homogeneous spaces with neg...

Let A and M be closed linear operators defined on a complex Banach space X. Using operator-valued Fourier multipliers theorems, we obtain necessary and sufficient conditions to guarantee existence and uniqueness of periodic solutions to the equation d dt (Mu(t)) = Au(t) + f(t), in terms of either boundedness or R-boundedness of the modified resolvent operator determined by the equation. Our res...