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A strong convergence theorem for H¹(𝕋ⁿ)

Feng Dai — 2006

Studia Mathematica

Let ⁿ denote the usual n-torus and let S ̃ u δ ( f ) , u > 0, denote the Bochner-Riesz means of order δ > 0 of the Fourier expansion of f ∈ L¹(ⁿ). The main result of this paper states that for f ∈ H¹(ⁿ) and the critical index α: = (n-1)/2, l i m R 1 / l o g R 0 R ( | | S ̃ u α ( f ) - f | | H ¹ ( ) ) / ( u + 1 ) d u = 0 .

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