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Anisotropic ornstein noninequalities. / Kazaniecki, Krystian; Stolyarov, Dmitriy M.; Wojciechowski, Michał.

In: Analysis and PDE, Vol. 10, No. 2, 01.01.2017, p. 351-366.

Research output: Contribution to journal › Article › peer-review

Harvard

Kazaniecki, K, Stolyarov, DM & Wojciechowski, M 2017, 'Anisotropic ornstein noninequalities', Analysis and PDE, vol. 10, no. 2, pp. 351-366. https://doi.org/10.2140/apde.2017.10.351

APA

Kazaniecki, K., Stolyarov, D. M., & Wojciechowski, M. (2017). Anisotropic ornstein noninequalities. Analysis and PDE, 10(2), 351-366. https://doi.org/10.2140/apde.2017.10.351

Vancouver

Kazaniecki K, Stolyarov DM, Wojciechowski M. Anisotropic ornstein noninequalities. Analysis and PDE. 2017 Jan 1;10(2):351-366. https://doi.org/10.2140/apde.2017.10.351

Author

Kazaniecki, Krystian ; Stolyarov, Dmitriy M. ; Wojciechowski, Michał. / Anisotropic ornstein noninequalities. In: Analysis and PDE. 2017 ; Vol. 10, No. 2. pp. 351-366.

BibTeX

@article{d7cec30e626746feb521dfea574299cd,
title = "Anisotropic ornstein noninequalities",
abstract = "We investigate the existence of a priori estimates for differential operators in the L1 norm: for anisotropic homogeneous differential operators T1, . . ., Tℓ, we study the conditions under which the inequality holds true. Properties of homogeneous rank-one convex functions play the major role in the subject. We generalize the notions of quasi- and rank-one convexity to fit the anisotropic situation. We also discuss a similar problem for martingale transforms and provide various conjectures.",
keywords = "Bellman function, Martingale transform, Ornstein noninequalities",
author = "Krystian Kazaniecki and Stolyarov, {Dmitriy M.} and Micha{\l} Wojciechowski",
year = "2017",
month = jan,
day = "1",
doi = "10.2140/apde.2017.10.351",
language = "English",
volume = "10",
pages = "351--366",
journal = "Analysis and PDE",
issn = "2157-5045",
publisher = "Mathematical Sciences Publishers",
number = "2",

}

RIS

TY - JOUR

T1 - Anisotropic ornstein noninequalities

AU - Kazaniecki, Krystian

AU - Stolyarov, Dmitriy M.

AU - Wojciechowski, Michał

PY - 2017/1/1

Y1 - 2017/1/1

N2 - We investigate the existence of a priori estimates for differential operators in the L1 norm: for anisotropic homogeneous differential operators T1, . . ., Tℓ, we study the conditions under which the inequality holds true. Properties of homogeneous rank-one convex functions play the major role in the subject. We generalize the notions of quasi- and rank-one convexity to fit the anisotropic situation. We also discuss a similar problem for martingale transforms and provide various conjectures.

AB - We investigate the existence of a priori estimates for differential operators in the L1 norm: for anisotropic homogeneous differential operators T1, . . ., Tℓ, we study the conditions under which the inequality holds true. Properties of homogeneous rank-one convex functions play the major role in the subject. We generalize the notions of quasi- and rank-one convexity to fit the anisotropic situation. We also discuss a similar problem for martingale transforms and provide various conjectures.

KW - Bellman function

KW - Martingale transform

KW - Ornstein noninequalities

UR - http://www.scopus.com/inward/record.url?scp=85014700764&partnerID=8YFLogxK

U2 - 10.2140/apde.2017.10.351

DO - 10.2140/apde.2017.10.351

M3 - Article

AN - SCOPUS:85014700764

VL - 10

SP - 351

EP - 366

JO - Analysis and PDE

JF - Analysis and PDE

SN - 2157-5045

IS - 2

ER -

ID: 35958526