Harmonic, Wavelet and P-Adic Analysis

Chuong, Nguyen Minh; Egorov, Yu. V.; Khrennikov, Andrei; Meyer, Yves; Mumford, David

doi:10.1142/6373

Cited by 33 publications

(10 citation statements)

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“…In [1,2], we use an orthonormal basis of functions that are eigenvectors of the Vladimirov's operator [9]. In this section we will introduce a new class of orthonormal basis in L 2 (Q p ) consisting of testing functions in Q p , very useful for researchers.…”

Section: A New Class Of Orthonormal Basis In L 2 (Q P )mentioning

confidence: 99%

The Cauchy problem for a class of pseudodifferential equations over p-adic field

Chuong

2008

Journal of Mathematical Analysis and Applications

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In this paper, some classes much more general than the one in [N.M. Chuong, Yu.V. Egorov, A. Khrennikov, Y. Meyer, D. Mumford (Eds.), Harmonic, Wavelet and p-Adic Analysis, World Scientific, Singapore, 2007] of Cauchy problems for an interesting class of pseudodifferential equations over p-adic fields are studied. The used functions belong to mixed classes of real and p-adic functions. Even for p-adic partial differential equations such problems in such function spaces have not been discussed yet. The established mathematical foundation requires very complicated and very difficult proofs. Days after days, these equations occur increasingly in mathematical physics, quantum mechanics. Explicit solutions of such problems are very needed for specialists on applied mathematics, physics, and engineering.

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Section: A New Class Of Orthonormal Basis In L 2 (Q P )mentioning

confidence: 99%

The Cauchy problem for a class of pseudodifferential equations over p-adic field

Chuong

2008

Journal of Mathematical Analysis and Applications

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“…From the integral theory it is easy to see that |B γ (a)| H = p nγ and |S γ (a)| H = p nγ (1p -n ) for any a ∈ Q n p . For a more complete introduction to the p-adic analysis, we refer to [1][2][3][4][5][6][7][8] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

p-adic singular integrals and their commutators in generalized Morrey spaces

Han

Yang

et al. 2019

J Inequal Appl

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“…On the other hand, it plays a crucial role in pseudo-di erential equations, wavelet theory and harmonic analysis, etc. (see [3][4][5][6][7]10]). …”

Section: Introductionmentioning

confidence: 99%

Weighted multilinear p-adic Hardy operators and commutators

Liu

Zhou

2017

Open Mathematics

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Abstract:In this paper, the weighted multilinear p-adic Hardy operators are introduced, and their sharp bounds are obtained on the product of p-adic Lebesgue spaces, and the product of p-adic central Morrey spaces, the product of p-adic Morrey spaces, respectively. Moreover, we establish the boundedness of commutators of the weighted multilinear p-adic Hardy operators on the product of p-adic central Morrey spaces. However, it's worth mentioning that these results are di erent from that on Euclidean spaces due to the special structure of the p-adic elds.

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Harmonic, Wavelet and P-Adic Analysis

Cited by 33 publications

References 0 publications

The Cauchy problem for a class of pseudodifferential equations over p-adic field

The Cauchy problem for a class of pseudodifferential equations over p-adic field

p-adic singular integrals and their commutators in generalized Morrey spaces

Weighted multilinear p-adic Hardy operators and commutators

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