Skip to main content
×
Home
    • Aa
    • Aa

Spherical averages of Fourier transforms of measures with finite energy; dimensions of intersections and distance sets

  • Pertti Mattila (a1)
Abstract

Let μ, be a positive Radon measure with compact support in the euclidean n-space ℝn. Introducing the Fourier transform

and the averages over the spheres

we can write the α-energy, 0 < α < n, of μ as

where the positive constants c1 and c2 depend only on n and α. The second equality is based on the Plancherel formula and the fact that where .

Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

K2.J.-P. Kahane . Sur la dimensions des intersections, Aspects of Mathematics and its Applications, J. A. Barroso editor (Elsevier Science Publishers B.V., 1986, 419430).

L.N. S. Landkof . Foundations of Modern Potential Theory (Springer, 1972).

M1.P. Mattila . Hausdorff dimension and capacities of intersections of sets in n-space. Acta Math., 152 (1984), 77105.

M.B. Muckenhoupt . Weighted norm inequalities for the Hardy maximal function. Trans. Amer. Math. Soc., 165 (1972), 207226.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematika
  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Keywords: