Displaying similar documents to “Correction to “Summability in ł ( p 1 , p 2 , . . . ) spaces” Studia Mathematica 25 (1965), p. 277-280)”

Necessary and sufficient Tauberian conditions for the logarithmic summability of functions and sequences

Ferenc Móricz (2013)

Studia Mathematica

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Let s: [1,∞) → ℂ be a locally Lebesgue integrable function. We say that s is summable (L,1) if there exists some A ∈ ℂ such that l i m t τ ( t ) = A , where τ ( t ) : = 1 / ( l o g t ) 1 t s ( u ) / u d u . (*) It is clear that if the ordinary limit s(t) → A exists, then also τ(t) → A as t → ∞. We present sufficient conditions, which are also necessary, in order that the converse implication hold true. As corollaries, we obtain so-called Tauberian theorems which are analogous to those known in the case of summability (C,1). For example, if the function...

Multi-dimensional Fejér summability and local Hardy spaces

Ferenc Weisz (2009)

Studia Mathematica

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It is proved that the multi-dimensional maximal Fejér operator defined in a cone is bounded from the amalgam Hardy space W ( h p , ) to W ( L p , ) . This implies the almost everywhere convergence of the Fejér means in a cone for all f W ( L , ) , which is larger than L ( d ) .

On the Nörlund means of Vilenkin-Fourier series

István Blahota, Lars-Erik Persson, Giorgi Tephnadze (2015)

Czechoslovak Mathematical Journal

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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...

A note on a critical problem with natural growth in the gradient

Boumediene Abdellaoui, Ireneo Peral (2006)

Journal of the European Mathematical Society

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The paper analyzes the influence on the meaning of natural growth in the gradient of a perturbation by a Hardy potential in some elliptic equations. Indeed, in the case of the Laplacian the natural problem becomes Δ u Λ N u | x | 2 = u + N 2 2 u | x | 2 x 2 | x | ( N 2 ) / 2 + λ f ( x ) in Ω , u = 0 on Ω , Λ N = ( ( N 2 ) / 2 ) 2 . This problem is a particular case of problem (2). Notice that ( N 2 ) / 2 is optimal as coefficient and exponent on the right hand side.

Solutions for the p-order Feigenbaum’s functional equation h ( g ( x ) ) = g p ( h ( x ) )

Min Zhang, Jianguo Si (2014)

Annales Polonici Mathematici

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This work deals with Feigenbaum’s functional equation ⎧ h ( g ( x ) ) = g p ( h ( x ) ) , ⎨ ⎩ g(0) = 1, -1 ≤ g(x) ≤ 1, x∈[-1,1] where p ≥ 2 is an integer, g p is the p-fold iteration of g, and h is a strictly monotone odd continuous function on [-1,1] with h(0) = 0 and |h(x)| < |x| (x ∈ [-1,1], x ≠ 0). Using a constructive method, we discuss the existence of continuous unimodal even solutions of the above equation.

On generalized absolute Cesaro summability factors

A. Nihal Tuncer (2002)

Annales Polonici Mathematici

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Using δ-quasi-monotone and any almost increasing sequences we prove a theorem on | C , α , β ; δ | k summability factors of infinite series, which generalizes a theorem of Mazhar [7] on | C , 1 | k summability factors.

Structure of Cesàro function spaces: a survey

Sergey V. Astashkin, Lech Maligranda (2014)

Banach Center Publications

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Geometric structure of Cesàro function spaces C e s p ( I ) , where I = [0,1] and [0,∞), is investigated. Among other matters we present a description of their dual spaces, characterize the sets of all q ∈ [1,∞] such that C e s p [ 0 , 1 ] contains isomorphic and complemented copies of l q -spaces, show that Cesàro function spaces fail the fixed point property, give a description of subspaces generated by Rademacher functions in spaces C e s p [ 0 , 1 ] .

Extensions of weak type multipliers

P. Mohanty, S. Madan (2003)

Studia Mathematica

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We prove that if Λ M p ( N ) and has compact support then Λ is a weak summability kernel for 1 < p < ∞, where M p ( N ) is the space of multipliers of L p ( N ) .