Interpolation of Operators in Hardy-Type Spaces
Informatics and Automation, Theory of Functions of Several Real Variables and Its Applications, Tome 323 (2023), pp. 181-195.

Voir la notice de l'article provenant de la source Math-Net.Ru

A number of statements similar to the Marcinkiewicz interpolation theorem are presented. The difference from the classical forms of this theorem is that the spaces of integrable functions are replaced by certain classes of functions that are extensions of various Hardy spaces.
Mots-clés : nontangent maximal function
Keywords: Hardy spaces, Marcinkiewicz interpolation theorem.
@article{TRSPY_2023_323_a9,
     author = {V. G. Krotov},
     title = {Interpolation of {Operators} in {Hardy-Type} {Spaces}},
     journal = {Informatics and Automation},
     pages = {181--195},
     publisher = {mathdoc},
     volume = {323},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2023_323_a9/}
}
TY  - JOUR
AU  - V. G. Krotov
TI  - Interpolation of Operators in Hardy-Type Spaces
JO  - Informatics and Automation
PY  - 2023
SP  - 181
EP  - 195
VL  - 323
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2023_323_a9/
LA  - ru
ID  - TRSPY_2023_323_a9
ER  - 
%0 Journal Article
%A V. G. Krotov
%T Interpolation of Operators in Hardy-Type Spaces
%J Informatics and Automation
%D 2023
%P 181-195
%V 323
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2023_323_a9/
%G ru
%F TRSPY_2023_323_a9
V. G. Krotov. Interpolation of Operators in Hardy-Type Spaces. Informatics and Automation, Theory of Functions of Several Real Variables and Its Applications, Tome 323 (2023), pp. 181-195. http://geodesic.mathdoc.fr/item/TRSPY_2023_323_a9/

[1] Aoki T., “Locally bounded linear topological spaces”, Proc. Imp. Acad. Tokyo, 18:10 (1942), 588–594 | MR | Zbl

[2] V. I. Bogachev, Measure Theory, v. 1, Springer, Berlin, 2007 | MR | Zbl

[3] Coifman R.R., Meyer Y., Stein E.M., “Some new function spaces and their applications to harmonic analysis”, J. Funct. Anal., 62:2 (1985), 304–335 | DOI | MR | Zbl

[4] Fefferman C., Stein E.M., “$H^p$ spaces of several variables”, Acta math., 129 (1972), 137–193 | DOI | MR | Zbl

[5] Grafakos L., Classical Fourier analysis, Grad. Texts Math., 249, 2nd ed., Springer, New York, 2008 | DOI | MR | Zbl

[6] Grafakos L., Classical Fourier analysis, Grad. Texts Math., 249, 3rd ed., Springer, New York, 2014 | MR | Zbl

[7] Grafakos L., Modern Fourier analysis, Grad. Texts Math., 250, 3rd ed., Springer, New York, 2014 | MR | Zbl

[8] Hardy G.H., Littlewood J.E., “A maximal theorem with function-theoretic applications”, Acta math., 54 (1930), 81–116 | DOI | MR

[9] V. G. Krotov, “On the boundary behavior of functions in spaces of Hardy type”, Math. USSR, Izv., 37:2 (1991), 303–320 | DOI | MR | MR | Zbl | Zbl

[10] V. G. Krotov, “Marcinkiewicz interpolation theorem for spaces of Hardy type”, Math. Notes, 113:1–2 (2023), 306–310 | DOI | DOI | MR | MR | Zbl

[11] Liang Y.Y., Liu L.G., Yang D.C., “An off-diagonal Marcinkiewicz interpolation theorem on Lorentz spaces”, Acta math. Sin. Engl. Ser., 27:8 (2011), 1477–1488 | DOI | MR | Zbl

[12] Lorentz G.G., “Some new functional spaces”, Ann. Math. Ser. 2, 51:1 (1950), 37–55 | DOI | MR | Zbl

[13] Marcinkiewicz J., “Sur l'interpolation d'operations”, C. r. Acad. sci. Paris, 208 (1939), 1272–1273 | Zbl

[14] Pipher J., Verchota G.C., “Dilation invariant estimates and the boundary Gårding inequality for higher order elliptic operators”, Ann. Math. Ser. 2, 142:1 (1995), 1–38 | DOI | MR | Zbl

[15] Rolewicz S., Metric linear spaces, Math. Appl. East Eur. Ser., 20, 2nd ed., D. Reidel Publ. Co., Dordrecht, 1985 | MR | Zbl

[16] W. Rudin, Function Theory in the Unit Ball of $\mathbb C^n$, Springer, Berlin, 1980 | MR | MR

[17] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, NJ, 1970 | MR | Zbl

[18] Stein E.M., Weiss G., “An extension of a theorem of Marcinkiewicz and some of its applications”, J. Math. Mech., 8:2 (1959), 263–284 | MR | Zbl

[19] E. M. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, NJ, 1971 | MR | Zbl

[20] Verchota G., “The Dirichlet problem for the polyharmonic equation in Lipschitz domains”, Indiana Univ. Math. J., 39:3 (1990), 671–702 | DOI | MR | Zbl

[21] Zygmund A., “On a theorem of Marcinkiewicz concerning interpolation of operations”, J. math. pures appl., 35 (1956), 223–248 | MR | Zbl

[22] A. Zygmund, Trigonometric Series, v. 2, Univ. Press, Cambridge, 1959 | MR | Zbl