Some weak type inequalities and almost everywhere convergence of Vilenkin-Norlund means

• We prove and discuss some new weak type (1,1) inequalities of maximal operators of Vilenkin-Norlund means generated by monotone coefficients. Moreover, we use these results to prove a.e. convergence of such Vilenkin-Norlund means. As applications, both some well-known and new inequalities are pointed out.

Subject headings

NATURVETENSKAP  -- Matematik -- Matematisk analys (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Mathematical Analysis (hsv//eng)

Keyword

Vilenkin system

Vilenkin group

Vilenkin-Fourier series

Norlund means

Martingale Hardy space

Weak - L-p spaces

Maximal operator

Weak type inequality

Matematik

Mathematics

Publication and Content Type

ref (subject category)

art (subject category)