On generalizations of theorems of Leindler

He, Jilong

doi:10.1007/s10474-013-0311-2

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2018

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“…We omit the proof, since the proof of this lemma follows the same line as that of Theorem 3.1. in [4], where (12) for the Fourier sine expansion is proved.…”

Section: Lemmasmentioning

confidence: 97%

Embedding relations of Besov classes under MVBV

Cheng¹,

Yu²,

Chen³

2018

Filomat

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In this paper, we strengthen some of Leindler's results from [L. Leindler. Embedding relations of Besov classes. Acta Sci. Math. (Szeged), 73(2007) 133-149.] under MVBV condition. First, we discuss embedding relations between two Besov classes. Next, we give an equivalent estimate for the k-order modulus of continuity of f (x) in L p norm under MVBV condition. Finally, we give the condition to ensure a function f ∈ L p having Fourier coefficients of MVBV belongs to the Besov class. n i≥n/2 a i , then γRBVS ≡ γ * MRBVS,

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“…We omit the proof, since the proof of this lemma follows the same line as that of Theorem 3.1. in [4], where (12) for the Fourier sine expansion is proved.…”

Section: Lemmasmentioning

confidence: 97%