English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this PhD thesis we discuss, develop and apply this fascinating theoryconnected to modern harmonic analysis. In particular we make new estimations ofVilenkin-Fourier coefficients and prove some new results concerning boundednessof maximal operators of partial sums. Moreover, we derive necessary andsufficient conditions for the modulus of continuity so that norm convergence ofthe partial sums is valid and develop new methods to prove Hardy typeinequalities for the partial sums with respect to the Vilenkin systems. We alsodo the similar investigation for the Fej\'er means. Furthermore, we investigatesome N\"orlund means but only in the case when their coefficients are monotone.Some well-know examples of N\"orlund means are Fej\'er means, Ces\`aro meansand N\"orlund logarithmic means. In addition, we consider Riesz logarithmicmeans, which are not example of N\"orlund means. It is also proved that theseresults are the best possible in a special sense. As applications both somewell-known and new results are pointed out.

Ph.D. Thesis-Martingale Hardy spaces and summability of the one dimensional Vilenkin-Fourier series