Home Weak interpolation for the lipschitz class
Article
Licensed
Unlicensed Requires Authentication

Weak interpolation for the lipschitz class

  • Benxamín Macía EMAIL logo and Francesc Tugores
Published/Copyright: April 28, 2017
Become an author with De Gruyter Brill

Abstract

We introduce and characterize interpolation sets in a weak sense for the Lipschitz class in the unit disc of the complex plane. Interpolation sets in the classical sense and in a strong sense for this space have already been examined.


(Communicated by Stanisława Kanas)


References

[1] Bruna, J.: Boundary interpolations sets for holomorphic functions smooth to the boundary and BMO, Trans. Amer. Math. Soc. 264 (1981), 391–409.10.1090/S0002-9947-1981-0603770-5Search in Google Scholar

[2] Bruna, J.—Nicolau, A.—Øyma, K.: A note on interpolation in the Hardy spaces of the unit disc, Proc. Amer. Math. Soc. 124 (1996), 1197–1204.10.1090/S0002-9939-96-03168-1Search in Google Scholar

[3] Bruna, J.—Tugores, F.: Free interpolation for holomorphic functions regular to the boundary, Pacific J. Math. 108 (1983), 31–49.10.2140/pjm.1983.108.31Search in Google Scholar

[4] Dyn’kin, E. M.: Free interpolation sets for Hölder classes, Math. USSR, Sb. 37 (1980), 97–117.10.1070/SM1980v037n01ABEH001944Search in Google Scholar

[5] Kotochigov, A. M.: Interpolation by analytic functions that are smooth up to the boundary, Zap. Nauchn. Sem. LOMI (in Russian) 30 (1972), 167–169.Search in Google Scholar

[6] Kronstadt, E. P.: Interpolating sequences for functions satisfying a Lipschitz condition, Pacific J. Math. 63 (1976), 169–177.10.2140/pjm.1976.63.169Search in Google Scholar

[7] Vasyunin, V. I.: Bases of eigensubspaces and non-classical interpolation problems, Funct. Anal. Appl. 9 (1975), 327–328.10.1007/BF01075882Search in Google Scholar

Received: 2014-5-1
Accepted: 2015-10-11
Published Online: 2017-4-28
Published in Print: 2017-4-25

© 2017 Mathematical Institute Slovak Academy of Sciences

Articles in the same Issue

  1. 10.1515/ms-2015-0200
  2. Zero-divisor graphs of lower dismantlable lattices I
  3. Some results on the intersection graph of submodules of a module
  4. Class number parities of compositum of quadratic function fields
  5. Examples of beurling prime systems
  6. Connection between multiplication theorem for Bernoulli polynomials and first factor hp
  7. On permutational invariance of the metric discrepancy results
  8. Evaluation of sums containing triple aerated generalized Fibonomial coefficients
  9. Linear algebraic proof of Wigner theorem and its consequences
  10. A note on groups with finite conjugacy classes of subnormal subgroups
  11. Groups with the same complex group algebras as some extensions of psl(2, pn)
  12. Klee-Phelps convex groupoids
  13. On analytic functions with generalized bounded Mocanu variation in conic domain with complex order
  14. Weak interpolation for the lipschitz class
  15. Generalized Padé approximants for plane condenser and distribution of points
  16. Three-variable symmetric and antisymmetric exponential functions and orthogonal polynomials
  17. Positive solutions of nonlocal integral BVPS for the nonlinear coupled system involving high-order fractional differential
  18. Existence of positive solutions for a nonlinear nth-order m-point p-Laplacian impulsive boundary value problem
  19. Dirichlet boundary value problem for differential equation with ϕ-Laplacian and state-dependent impulses
  20. On the oscillation of certain third order nonlinear dynamic equations with a nonlinear damping term
  21. Homoclinic solutions for ordinary (q, p)-Laplacian systems with a coercive potential
  22. Semi-equivelar maps on the torus and the Klein bottle with few vertices
  23. A problem considered by Friedlander & Iwaniec and the discrete Hardy-Littlewood method
Downloaded on 24.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/ms-2016-0278/html
Scroll to top button