Canonical Sobolev projections of weak type (1, 1). Memoirs of the American Mathematical Society; no. 714 = March 2001, no. 5 = vol. 150, no. 5.

Berkson, Earl:

ISBN 10: 0821826654 / ISBN 13: 9780821826652

Edité par Providence, American Mathematical Society, 2001

A propos de cet article

Ex-library with stamp and library-signature. GOOD condition, some traces of use. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. C-05542 9780821826652 Sprache: Englisch Gewicht in Gramm: 550.

N° de réf. du vendeur 2491796

Détails bibliographiques

• Titre: Canonical Sobolev projections of weak type (1, 1). Memoirs of the American Mathematical Society; no. 714 = March 2001, no. 5 = vol. 150, no. 5.
• Éditeur: Providence, American Mathematical Society
• Date de parution: 2001
• Langue: anglais
• ISBN à 10 chiffres: 0821826654
• ISBN à 13 chiffres: 9780821826652
• Reliure: Softcover
• État de l'article: Gut
• Poids: 550 grammes
• Catalogues du vendeur:
  • SA MATHEMATIK

A propos de ce titre

Synopsis

Let $\mathcal S$ be a second order smoothness in the $\mathbb{R}^n$ setting. We can assume without loss of generality that the dimension $n$ has been adjusted as necessary so as to insure that $\mathcal S$ is also non-degenerate. We describe how $\mathcal S$ must fit into one of three mutually exclusive cases, and in each of these cases we characterize by a simple intrinsic condition the second order smoothnesses $\mathcal S$ whose canonical Sobolev projection $P_{\mathcal{S}}$ is of weak type $(1,1)$ in the $\mathbb{R}^n$ setting. In particular, we show that if $\mathcal S$ is reducible, $P_{\mathcal{S}}$ is automatically of weak type $(1,1)$. We also obtain the analogous results for the $\mathbb{T}^n$ setting.We conclude by showing that the canonical Sobolev projection of every $2$-dimensional smoothness, regardless of order, is of weak type $(1,1)$ in the $\mathbb{R}^2$ and $\mathbb{T}^2$ settings. The methods employed include known regularization, restriction, and extension theorems for weak type $(1,1)$ multipliers, in conjunction with combinatorics, asymptotics, and real variable methods developed below. One phase of our real variable methods shows that for a certain class of functions $f\in L^{\infty}(\mathbb R)$, the function $(x_1,x_2)\mapsto f(x_1x_2)$ is not a weak type $(1,1)$ multiplier for $L^({\mathbb R}^2)$.