Displaying similar documents to “On the inclusion relation between strong ( J , p n ) and strong ( N ¯ , p n ) summability methods”

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...

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 , ℓ ∞ ) to W ( L p , ℓ ∞ ) . This implies the almost everywhere convergence of the Fejér means in a cone for all f ∈ W ( L ₁ , ℓ ∞ ) , which is larger than L ₁ ( ℝ d ) .

Extensions of weak type multipliers

P. Mohanty, S. Madan (2003)

Studia Mathematica

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

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.

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...

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.

Pointwise Fourier inversion of distributions on spheres

Francisco Javier González Vieli (2017)

Czechoslovak Mathematical Journal

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Given a distribution T on the sphere we define, in analogy to the work of Łojasiewicz, the value of T at a point ξ of the sphere and we show that if T has the value τ at ξ , then the Fourier-Laplace series of T at ξ is Abel-summable to τ .