| 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, David, et al.
(författare)
-
Some New Weak (Hp- Lp) -Type Inequality for Weighted Maximal Operators of Partial Sums of Walsh–Fourier Series
- 2023
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Ingår i: Mediterranean Journal of Mathematics. - : Springer. - 1660-5446 .- 1660-5454. ; 20:5
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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 Hp(G) to the Lebesgue space weak - Lp(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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| 6. |
- 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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| 7. |
- 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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| 8. |
- 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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| 9. |
- 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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| 10. |
- 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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