1. |
- Baramidze, David, et al.
(författare)
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(H-p - L-p)-Type inequalities for subsequences of Norlund means of Walsh-Fourier series
- 2023
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Ingår i: Journal of inequalities and applications. - : Springer. - 1025-5834 .- 1029-242X. ; 2023:1
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Tidskriftsartikel (refereegranskat)abstract
- We investigate the subsequence {t2n f} of Norlund means with respect to the Walsh system generated by nonincreasing and convex sequences. In particular, we prove that a large class of such summability methods are not bounded from the martingale Hardy spaces H-p to the space weak-Lp for 0 < p < 1/(1+ alpha), where 0 < alpha < 1. Moreover, some new related inequalities are derived. As applications, some well-known and new results are pointed out for well-known summability methods, especially for Norlund logarithmic means and Cesaro means.
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2. |
- Baramidze, Davit, et al.
(författare)
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Some new (H-p - L-p) type inequalities for weighted maximal operators of partial sums of Walsh-Fourier series
- 2023
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Ingår i: Positivity (Dordrecht). - : Springer. - 1385-1292 .- 1572-9281. ; 27:3
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we introduce some new weighted maximal operators of the partial sums of the Walsh-Fourier series. We prove that for some "optimal" weights these new operators indeed are bounded from the martingale Hardy space H-p(G) to the Lebesgue space L-p(G), for 0 < p < 1. Moreover, we also prove sharpness of this result. As a consequence we obtain some new and well-known results.
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3. |
- Baramidze, Davit, et al.
(författare)
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Some new restricted maximal operators of Fejér means of Walsh–Fourier series
- 2023
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Ingår i: Banach Journal of Mathematical Analysis. - : Birkhäuser Verlag. - 1735-8787. ; 17
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we derive the maximal subspace of natural numbers nk: k≥ 0 , such that the restricted maximal operator, defined by supk∈N|σnkF| on this subspace of Fejér means of Walsh–Fourier series is bounded from the martingale Hardy space H1 / 2 to the Lebesgue space L1 / 2. The sharpness of this result is also proved.
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4. |
- Baramidze, David, et al.
(författare)
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Some new results and inequalities for subsequences of Nörlund logarithmic means of Walsh-Fourier series
- 2022
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Ingår i: Journal of inequalities and applications. - : Springer. - 1025-5834 .- 1029-242X.
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Tidskriftsartikel (refereegranskat)abstract
- We prove that there exists a martingale f is an element of H-p such that the subsequence {L(2n)f} of Norlund logarithmic means with respect to the Walsh system are not bounded from the martingale Hardy spaces H-p to the space weak - L-p for 0 < p < 1. We also prove that for any f is an element of L-p, p >= 1, L-2n f converge to f at any Lebesgue point x. Moreover, some new related inequalities are derived.
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5. |
- Baramidze, Davit, et al.
(författare)
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Some weak type inequalities and almost everywhere convergence of Vilenkin-Norlund means
- 2023
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Ingår i: Journal of inequalities and applications. - : Springer. - 1025-5834 .- 1029-242X. ; 2023:1
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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6. |
- Baramidze, Lasha, et al.
(författare)
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Sharp Hp- Lptype inequalities of weighted maximal operators of Vilenkin-Nörlund means and its applications
- 2016
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Ingår i: Journal of inequalities and applications. - : Springer Science and Business Media LLC. - 1025-5834 .- 1029-242X. ; :1
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Tidskriftsartikel (refereegranskat)abstract
- We prove and discuss some new Hp-Lptype inequalities of weighted maximal operators of Vilenkin-Nörlund means with monotone coefficients. It is also proved that these inequalities are the best possible in a special sense. We also apply these results to prove strong summability for such Vilenkin-Nörlund means. As applications, both some well-known and new results are pointed out
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7. |
- Blahota, István, et al.
(författare)
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A note on maximal operators of Vilenkin-Nörlund means
- 2016
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Ingår i: Acta Mathematica Academiae Paedagogiace Nyíregyháziensis. - 1786-0091. ; 32:2, s. 203-213
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we prove and discuss some new (Hp;Lp)-type inequalities of weighted maximal operators of Vilenkin - Nörlund means with non-increasing coeffcients. These results are the best possible in a special sense. As applications, both some well-known and new results are pointed out in the theory of strong convergence of Vilenkin - Nörlund means with non-increasing coeffcients
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8. |
- Blahota, István, et al.
(författare)
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On the (C, α)-means with respect to the Walsh system
- 2014
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Ingår i: Analysis Mathematica. - : Springer Science and Business Media LLC. - 0133-3852 .- 1588-273X. ; 40:3, s. 161-174
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Tidskriftsartikel (refereegranskat)abstract
- In our main result we prove strong convergence theorems for Cesàro means (C, α) on the Hardy spaces H1/(1+α), where 0 < α < 1. © 2014 Akadémiai Kiadó, Budapest, Hungary.
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9. |
- Blahota, István, et al.
(författare)
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On the Nörlund means of Vilenkin-Fourier series
- 2015
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Ingår i: Czechoslovak Mathematical Journal. - : Institute of Mathematics, Czech Academy of Sciences. - 0011-4642 .- 1572-9141. ; 65:4, s. 983-1002
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Tidskriftsartikel (refereegranskat)abstract
- We prove and discuss some new (H p ,L p )-type inequalities of weighted maximal operators of Vilenkin-Nörlund means with non-increasing coefficients {q k : k ⩾ 0}. These results are the best possible in a special sense. As applications, some well-known as well as new results are pointed out in the theory of strong convergence of such Vilenkin-Nörlund means. To fulfil our main aims we also prove some new estimates of independent interest for the kernels of these summability results.In the special cases of general Nörlund means t n with non-increasing coefficients analogous results can be obtained for Fejér and Cesàro means by choosing the generating sequence {q k : k ⩾ 0} in an appropriate way.
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10. |
- Blahota, István, et al.
(författare)
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Strong convergence theorem for Vilenkin-Fejér means
- 2014
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Ingår i: Publicationes mathematicae (Debrecen). - 0033-3883 .- 2064-2849. ; 85:1-2, s. 181-196
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Tidskriftsartikel (refereegranskat)abstract
- As main result we prove strong convergence theorems of Vilenkin- Fejér means when 0 < p ≤ 1/2.
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