We investigate existence of a priori estimates for differential operators in L 1 norm: for anisotropic homogeneous differential operators T1, . . . , T ℓ , we study the conditions under which the inequalityholds true. We also discuss a similar problem for martingale transforms.
Abstract. In this paper we proof that every Fourier multiplier on homogeneous Sobolev spaceẆ 1 1 (R d ) is a continuous function. This theorem is generalization of A. Bonami and S. Poornima result for Fourier multipliers, which are homogeneous functions of degree zero.
Abstract. We prove an ε-regularity result for a wide class of parabolic systemswith the right hand side B growing critically, like |∇u| p . It is assumed a priori that the solution u(t, ·) is uniformly small in the space of functions of bounded mean oscillation. The crucial tool is provided by a sharp nonlinear version of the Gagliardo-Nirenberg inequality which has been used earlier in the elliptic context by T. Rivière and the last named author.
In this paper we construct an injection from the linear space of trigonometric polynomials defined on T d with bounded degrees with respect to each variable to a suitable linear subspace L 1 E ⊂ L 1 (T). We give such a quantitative condition on L 1 E that this injection is a isomorphism of a Banach spaces equipped with L 1 norm and the norm of the isomorphism is independent on the dimension d.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.