Spherical square functions of Marcinkiewicz type with Riesz potentials

DOI10.1007/s00013-017-1027-2zbMath1364.42024OpenAlexW2594688194MaRDI QIDQ527301

Shuichi Sato

Publication date: 11 May 2017

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://kanazawa-u.repo.nii.ac.jp/?action=repository_action_common_download&item_id=956&item_no=1&attribute_id=26&file_no=1

zbMATH Keywords

Sobolev spaceLittlewood-Paley functionRiesz potentialBochner-Riesz operatorsMarcinkiewicz function

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) Function spaces arising in harmonic analysis (42B35) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35)

Related Items (5)

Sobolev spaces with non-isotropic dilations and square functions of Marcinkiewicz type ⋮ Characterization of \(H^1\) Sobolev spaces by square functions of Marcinkiewicz type ⋮ Weak type estimates for functions of Marcinkiewicz type with fractional integrals of mixed homogeneity ⋮ Pointwise Characterizations of Even Order Sobolev Spaces via Derivatives of Ball Averages ⋮ Sobolev spaces and functions of Marcinkiewicz type with repeated averaging operations over spheres

Cites Work

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• A new characterization of Sobolev spaces on \({\mathbb{R}^{n}}\)
• A Marcinkiewicz integral type characterization of the Sobolev space
• Littlewood-Paley operators and Sobolev spaces
• On the Littlewood-Paley and Marcinkiewicz functions in higher dimensions
• On an Integral of Marcinkiewicz
• Remarks on square functions in the Littlewood-Paley theory
• On Certain Integrals

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