The Calderón-Zygmund theorem and parabolic equations in L P ( ℝ , C 2 + α ) -spaces

Nicolai V. Krylov

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2002)

  • Volume: 1, Issue: 4, page 799-820
  • ISSN: 0391-173X

Abstract

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A Banach-space version of the Calderón-Zygmund theorem is presented and applied to obtaining apriori estimates for solutions of second-order parabolic equations in L p ( ℝ , C 2 + α ) -spaces.

How to cite

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Krylov, Nicolai V.. "The Calderón-Zygmund theorem and parabolic equations in $L P (\mathbb {R}, C^{2+\alpha })$-spaces." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 1.4 (2002): 799-820. <http://eudml.org/doc/84487>.

@article{Krylov2002,
abstract = {A Banach-space version of the Calderón-Zygmund theorem is presented and applied to obtaining apriori estimates for solutions of second-order parabolic equations in $L_\{p\}(\mathbb \{R\},C^\{2+\alpha \})$-spaces.},
author = {Krylov, Nicolai V.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {4},
pages = {799-820},
publisher = {Scuola normale superiore},
title = {The Calderón-Zygmund theorem and parabolic equations in $L P (\mathbb \{R\}, C^\{2+\alpha \})$-spaces},
url = {http://eudml.org/doc/84487},
volume = {1},
year = {2002},
}

TY - JOUR
AU - Krylov, Nicolai V.
TI - The Calderón-Zygmund theorem and parabolic equations in $L P (\mathbb {R}, C^{2+\alpha })$-spaces
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2002
PB - Scuola normale superiore
VL - 1
IS - 4
SP - 799
EP - 820
AB - A Banach-space version of the Calderón-Zygmund theorem is presented and applied to obtaining apriori estimates for solutions of second-order parabolic equations in $L_{p}(\mathbb {R},C^{2+\alpha })$-spaces.
LA - eng
UR - http://eudml.org/doc/84487
ER -

References

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  1. [1] A. Brandt, Interior Schauder estimates for parabolic differential- (or difference- ) equations via the maximum principle, Israel J. Math. 7 (1969), 254-262. Zbl0184.32304MR249803
  2. [2] B. F. Jones, A class of singular integrals, Amer. J. Math. 86 (1964), 441-462. Zbl0123.08501MR161099
  3. [3] B. Knerr, Parabolic interior Schauder estimates by the maximum principle, Arch. Rational Mech. Anal. 75 (1980), 51-58. Zbl0468.35014MR592103
  4. [4] N. V. Krylov, A parabolic Littlewood-Paley inequality with applications to parabolic equations, Topological Methods in Nonlinear Analysis, Journal of the Juliusz Schauder Center 4 (1994), 355-364. Zbl0839.35017MR1350977
  5. [5] N. V. Krylov, “Lectures on elliptic and parabolic equations in Hölder spaces”, Amer. Math. Soc., Providence, RI, 1996. Zbl0865.35001MR1406091
  6. [6] N. V. Krylov, The heat equation in L q ( ( 0 , T ) , L p ) -spaces with weights, SIAM J. Math. Anal. 32 (2001), 117-1141. Zbl0979.35060MR1828321
  7. [7] N. V. Krylov, On the Calderón-Zygmund theorem with applications to parabolic equations, Algebra i Analiz 13 (2001), 1-25, in Russian; English translation in St Petersburg Math. J. 13 (2002), 509-526. Zbl1011.35033MR1865493
  8. [8] N. V. Krylov, Parabolic equations in L p -spaces with mixed norms, to appear in Algebra i Analiz. Zbl1032.35046
  9. [9] L. Lorenzi, Optimal Schauder estimates for parabolic problems with data measurable with respect to time, SIAM J. Math. Anal. 32 (2000), 588-615. Zbl0974.35018MR1786159
  10. [10] A. Lunardi, An interpolation method to characterize domains of generators of semigroups, Semigroup Forum 53 (1996), 321-329. Zbl0859.47030MR1406778
  11. [11] E. M. Stein, “Harmonic analysis: real-variable methods, orthogonality and oscillatory integrals”, Princeton Univ. Press, Princeton, NJ, 1993. Zbl0821.42001MR1232192

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