Intro
Preface
How to Read the Book?
Acknowledgements
Contents
1 Partial Sums of Vilenkin-Fourier Series in Lebesgue Spaces
1.1 Introduction
1.2 Vilenkin Groups and Functions
1.3 The Representation of the Vilenkin Groups on the Interval [0,1)
1.4 Convex Functions and Classical Inequalities
1.5 Lebesgue Spaces
1.6 Dirichlet Kernels
1.7 Lebesgue Constants
1.8 Vilenkin-Fourier Coefficients
1.9 Partial Sums
1.10 Final Comments and Open Questions
2 Martingales and Almost Everywhere Convergence of Partial Sums of Vilenkin-Fourier Series
2.1 Introduction
2.2 Conditional Expectation Operators
2.3 Martingales and Maximal Functions
2.4 Calderon-Zygmund Decomposition
2.5 Almost Everywhere Convergence of Vilenkin-Fourier Series
2.6 Almost Everywhere Divergence of Vilenkin-Fourier Series
2.7 Final Comments and Open Questions
3 Vilenkin-Fejér Means and an Approximate Identity in Lebesgue Spaces
3.1 Introduction
3.2 Vilenkin-Fejér Kernels
3.3 Approximation of Vilenkin-Fejér Means
3.4 Almost Everywhere Convergence of Vilenkin- Fejér Means
3.5 Approximate Identity
3.6 Final Comments and Open Questions
4 Nörlund and T Means of Vilenkin-Fourier Series in Lebesgue Spaces
4.1 Introduction
4.2 Well-Known and New Examples of Nörlund and TMeans
4.3 Regularity of Nörlund and T Means
4.4 Kernels of Nörlund Means
4.5 Kernels of T Means
4.6 Norm Convergence of Nörlund and T Means in Lebesgue Spaces
4.7 Almost Everywhere Convergence of Nörlund and T Means
4.8 Convergence of Nörlund and T Means in Vilenkin-Lebesgue Points
4.9 Riesz and Nörlund Logarithmic Kernels and Means
4.10 Final Comments and Open Questions
5 Theory of Martingale Hardy Spaces
5.1 Introduction
5.2 Martingale Hardy Spaces and Modulus of Continuity.

9.7 Atomic Decomposition of Variable Hardy Spaces
9.8 Martingale Inequalities in Variable Spaces
9.9 Partial Sums of Vilenkin-Fourier Series in Variable Lebesgue Spaces
9.10 The Maximal Fejér Operator on Hp(·)
9.11 Final Comments and Open Questions
10 Appendix: Dyadic Group and Walsh and Kaczmarz Systems
10.1 Introduction
10.2 Walsh Group and Walsh and Kaczmarz Systems
10.3 Estimates of the Walsh-Fejér Kernels
10.4 Walsh-Fejér Means in Hp
10.5 Modulus of Continuity in Hp and Walsh-Fejér Means
10.6 Riesz and Nörlund Logarithmic Means in Hp
10.7 Maximal Operators of Kaczmarz-Fejér Means on Hp
10.8 Modulus of Continuity in Hp and Kaczmarz-Fejér Means
10.9 Final Comments and Open Questions
References
Notations
Index.