L^2-bounded singular integrals on a purely unrectifiable set in R^d

Kirjoittajat

  • Joan Mateu Universitat Autònoma de Barcelona, Departament de Matemàtiques and Centre de Reserca Matemàtica
  • Laura Prat Universitat Autònoma de Barcelona, Departament de Matemàtiques and Centre de Reserca Matemàtica

Avainsanat:

Purely unrectifiable set, singular integral operator, Cantor type set, T(1)-theorem

Abstrakti

We construct an example of a purely unrectifiable measure μ in Rd for which the singular integrals associated to the kernels K(x)=P2k+1(x)/|x|2k+d, with k1 and P2k+1 a homogeneous harmonic polynomial of degree 2k+1, are bounded in L2(μ). This contrasts starkly with the results concerning the Riesz kernel x/|x|d in Rd.
Osasto
Articles

Julkaistu

2021-06-24

Viittaaminen

Mateu, J., & Prat, L. (2021). L^2-bounded singular integrals on a purely unrectifiable set in R^d. Annales Fennici Mathematici, 46(1), 187–200. Noudettu osoitteesta https://afm.journal.fi/article/view/109766