The Calderón-Zygmund theorem and parabolic equations in LP(,C 2+α )-spaces
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 1 (2002) no. 4, p. 799-820

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 (,C 2+α )-spaces.

Classification:  35K10,  35J15
@article{ASNSP_2002_5_1_4_799_0,
     author = {Krylov, Nicolai V.},
     title = {The Calder\'on-Zygmund theorem and parabolic equations in $L P (\mathbb {R}, C^{2+\alpha })$-spaces},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 5, 1},
     number = {4},
     year = {2002},
     pages = {799-820},
     zbl = {pre05019622},
     mrnumber = {1991003},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2002_5_1_4_799_0}
}
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, Serie 5, Volume 1 (2002) no. 4, pp. 799-820. http://www.numdam.org/item/ASNSP_2002_5_1_4_799_0/

[1] A. Brandt, Interior Schauder estimates for parabolic differential- (or difference-) equations via the maximum principle, Israel J. Math. 7 (1969), 254-262. | MR 249803 | Zbl 0184.32304

[2] B. F. Jones, A class of singular integrals, Amer. J. Math. 86 (1964), 441-462. | MR 161099 | Zbl 0123.08501

[3] B. Knerr, Parabolic interior Schauder estimates by the maximum principle, Arch. Rational Mech. Anal. 75 (1980), 51-58. | MR 592103 | Zbl 0468.35014

[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. | MR 1350977 | Zbl 0839.35017

[5] N. V. Krylov, “Lectures on elliptic and parabolic equations in Hölder spaces”, Amer. Math. Soc., Providence, RI, 1996. | MR 1406091 | Zbl 0865.35001

[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. | MR 1828321 | Zbl 0979.35060

[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. | MR 1865493 | Zbl 1011.35033

[8] N. V. Krylov, Parabolic equations in L p -spaces with mixed norms, to appear in Algebra i Analiz. | Zbl 1032.35046

[9] L. Lorenzi, Optimal Schauder estimates for parabolic problems with data measurable with respect to time, SIAM J. Math. Anal. 32 (2000), 588-615. | MR 1786159 | Zbl 0974.35018

[10] A. Lunardi, An interpolation method to characterize domains of generators of semigroups, Semigroup Forum 53 (1996), 321-329. | MR 1406778 | Zbl 0859.47030

[11] E. M. Stein, “Harmonic analysis: real-variable methods, orthogonality and oscillatory integrals”, Princeton Univ. Press, Princeton, NJ, 1993. | MR 1232192 | Zbl 0821.42001