This paper gives a systematic study of Sobolev, Besov and Triebel-Lizorkin spaces on a
noncommutative d-torus Td θ (with θ a skew symmetric real d× d-matrix). These spaces …

Following an approach of the second author (Rivière,) for conformally invariant variational
problems in two dimensions, we show in four dimensions the existence of a conservation …

The paper provides a detailed study of crucial inequalities for smoothness and interpolation
characteristics in rearrangement invariant Banach function spaces. We present a unified …

Let $\mathcal {W} $ be a closed dilation and translation invariant subspace of the space of
$\mathbb {R}^\ell $-valued Schwartz distributions in $ d $ variables. We show that if the …

We prove a family of Sobolev inequalities of the form $$\Vert u\Vert_ {L^{\frac {n}{n-1},
1}(\mathbb {R}^ n, V)}\le\Vert A (D) u\Vert_ {L^ 1 (\mathbb {R}^ n, E)} $$ where $ A (D) …

In the 1930's, JE Littlewood and SL Sobolev each found useful estimates for L p-norms.
These results are usually not regarded as similar, because one of them is set in a discrete …

In this paper we propose a unified approach, based on limiting interpolation, to investigate
the embeddings for the Sobolev space $(\dot {W}^ k_p (\mathcal {X})) _0,\,\mathcal …

We consider Dirichlet problems for linear elliptic equations of second order in divergence
form on a bounded or exterior smooth domain Ω in R^n, n≥3, with drifts b in the critical weak …

Let E be a Banach space. Let $ L¹_ {(1)}(ℝ^ d, E) $ be the Sobolev space of E-valued
functions on $ ℝ^ d $ with the norm $ ʃ_ {ℝ^ d}∥ f∥ _E dx+ ʃ_ {ℝ^ d}∥∇ f∥ _E dx=∥ f∥ …

This paper is devoted to embedding theorems for classes of functions of several variables.
One of our main objectives is to give an analysis of some basic embeddings as well as to …