Construction de p-multiplicateurs

ArticleOriginal scientific text

Title

Authors ¹

Using characteristic functions of polyhedra, we construct radial p-multipliers which are continuous over

ℝ^{n}

but not continuously differentiable through

S^{n - 1}

and give a p-multiplier criterion for homogeneous functions over

ℝ^{2}

. We also exhibit fractal p-multipliers over the real line.

[EG] R. E. Edwards and G. I. Gaudry, Littlewood-Paley and Multiplier Theory, Springer, Berlin 1977.
[Fa] K. Falconer, Fractal Geometry, Wiley, Chichester 1990.
[Fe] C. Fefferman, The multiplier problem for the ball, Ann. of Math. 94 (1971), 330-336.
[H] L. Hörmander, Estimates for translation invariant operators in $L^{p}$ spaces, Acta Math. 104 (1960), 94-140.
[L] R. Larsen, An Introduction to the Theory of Multipliers, Springer, New York 1971.
[dL] K. de Leeuw, On $L_{p}$ multipliers, Ann. of Math. 81 (1965), 364-379.
[Ł] S. Łojasiewicz, An Introduction to the Theory of Real Functions, Wiley, Chichester 1988.
[St] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton University Press, 1970.