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Title of Journal: Acta Math Hung

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Abbravation: Acta Mathematica Hungarica

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Springer Netherlands

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DOI

10.1002/jctb.5000291005

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1588-2632

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A weak type inequality for the maximal operator of

Authors: Gy Gát U Goginava
Publish Date: 2009/05/08
Volume: 125, Issue: 1-2, Pages: 65-
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Abstract

Simon 12 proved that the maximal operator of C αmeans of Fourier series with respect to the WalshKaczmarz system is bounded from the martingale Hardy space H p to the space L p for p 1/1 + α In this paper we prove that this boundedness result does not hold if p ≦ 1/1 + α However in the endpoint case p = 1/1 + α the maximal operator σ αk is bounded from the martingale Hardy space H 1/1+α to the space weakL 1/1+α

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Other Papers In This Journal:
  1. Weightable quasi-uniformities
  2. Rings of quotients of some infinite dimensional path algebras
  3. The Baum–Katz theorem for dependent sequences
  4. On complete convergence in mean for double sums of independent random elements in Banach spaces
  5. A note on the generalized rank reduction
  6. Existence and optimality of w -non-adjacent forms with an algebraic integer base
  7. Veldsman’s classes of associative rings
  8. Atomic decompositions of martingale hardy–morrey spaces
  9. A characterization of polyharmonic functions
  10. A note on invariant sets of iterated function systems
  11. On complete convergence and the strong law of large numbers for pairwise independent random variables
  12. Polynomial approximation with an exponential weight on the real semiaxis
  13. Best L 1 Approximation of Truncated Functions, Whitney-Type and Borh–Favard-Type Inequalities
  14. On the latticity of projection and antiprojection sets in Orlicz-Musielak spaces
  15. A categorical approach to absolute closure
  16. Planar zero divisor graphs of partially ordered sets
  17. On a problem in additive number theory
  18. On powers of relational and algebraic systems
  19. Inequalities for entire functions of exponential type satisfying $$ f(z) \equiv e^{i\gamma } e^{i\tau z} \overline {f(\bar z)} $$
  20. Local stability of a generalized Cauchy equation in Banach spaces
  21. A note on W - I -continuous functions
  22. A Remark on The Geometry of Spaces of Functions with Prime Frequencies
  23. Hua’s theorem with nine almost equal prime variables
  24. Unification of generalized open sets on topological spaces
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