A new ℓ₁ estimate and a problem of Katznelson

Newman, D. J.

doi:10.1090/S0002-9939-1972-0296588-7

A new $\ell _{1}$ estimate and a problem of Katznelson
HTML articles powered by AMS MathViewer

by D. J. Newman

Proc. Amer. Math. Soc. 31 (1972), 225-227

DOI: https://doi.org/10.1090/S0002-9939-1972-0296588-7

PDF | Request permission

Abstract:

We produce a new estimate on the ${l_1}$ norm in terms of the closeness of approximation by functions with small derivatives. We thereby solve a problem of Katznelson and give new proofs of some old ${l_1}$ estimates.

References

Shmuel Agmon, Lectures on elliptic boundary value problems, Van Nostrand Mathematical Studies, No. 2, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London, 1965. Prepared for publication by B. Frank Jones, Jr. with the assistance of George W. Batten, Jr. MR 0178246
Lipman Bers, Fritz John, and Martin Schechter, Partial differential equations, Lectures in Applied Mathematics, vol. 3, American Mathematical Society, Providence, R.I., 1979. With supplements by Lars Gȧrding and A. N. Milgram; With a preface by A. S. Householder; Reprint of the 1964 original. MR 598466
Djairo Guedes de Figueiredo, The coerciveness problem for forms over vector valued functions, Comm. Pure Appl. Math. 16 (1963), 63–94. MR 149082, DOI 10.1002/cpa.3160160109

Dirichlet’s problem for linear elliptic partial differential equations

1

16

Les méthodes directes en théorie des équations elliptiques

37

James M. Newman, Coercive inequalities for sectors in the plane, Comm. Pure Appl. Math. 22 (1969), 825–838. MR 268505, DOI 10.1002/cpa.3160220606
Martin Schechter, Coerciveness of linear partial differential operators for functions satisfying zero Dirichlet-type boundary data, Comm. Pure Appl. Math. 11 (1958), 153–174. MR 132911, DOI 10.1002/cpa.3160110202
K. T. Smith, Inequalities for formally positive integro-differential forms, Bull. Amer. Math. Soc. 67 (1961), 368–370. MR 142895, DOI 10.1090/S0002-9904-1961-10622-8