Pointwise multiplication in the realized homogeneous Besov and Triebel--Lizorkin spaces
Problemy analiza, Tome 7 (2018) no. 1, pp. 3-22.

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For either homogeneous Besov spaces $\dot B_{p,q}^s(\mathbb{R}^n)$ or homogeneous Triebel–Lizorkin spaces $\dot F_{p,q}^s(\mathbb{R}^n)$, with the conditions either $s n/p$, or $s = n/p$ and $q \le 1$ in the $\dot B_{p,q}^s$-case, $p \le 1$ in the $\dot F_{p,q}^s$-case, we prove some pointwise multiplication assertions in their realized spaces.
Keywords: homogeneous Besov space; homogeneous Triebel–Lizorkin space; pointwise multiplication; realization.
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Samira Bissar; Madani Moussai. Pointwise multiplication in the realized homogeneous Besov and  Triebel--Lizorkin spaces. Problemy analiza, Tome 7 (2018) no. 1, pp. 3-22. http://geodesic.mathdoc.fr/item/PA_2018_7_1_a0/

[1] Bergh G., Löfström J., Interpolation Theory, An Introduction, Grundlehren Math. Wiss., 223, Springer, Berlin, 1976 | DOI | MR

[2] Bourdaud G., “Réalisations des espaces de Besov homogènes”, Ark. Mat., 26 (1988), 41–54 | DOI | MR | Zbl

[3] Bourdaud G., “Realizations of homogeneous Besov and Lizorkin-Triebel spaces”, Math. Nachr., 286 (2013), 476–491 | DOI | MR | Zbl

[4] Bourdaud G., Moussai M., Sickel W., “Composition operators in Lizorkin-Triebel spaces”, J. Funct. Anal., 259 (2010), 1098–1128 | DOI | MR | Zbl

[5] Fefferman C., Stein E. M., “Some maximal inequalities”, Amer. J. Math., 93 (1971), 107–115 | DOI | MR | Zbl

[6] Franke J., “On the spaces $F^s_{p,q}$ of Triebel-Lizorkin type: Pointwise multipliers and spaces on domains”, Math. Nachr., 125 (1986), 29–68 | DOI | MR | Zbl

[7] Frazier M., Jawerth B., Weiss G., Littlewood-Paley Theory and the Study of Function Spaces, CBMS-AMS Regional Conference Series, 79, 1991 | DOI | MR | Zbl

[8] Jawerth B., “Some observations on Besov and Triebel-Lizorkin spaces”, Math. Scand., 40 (1977), 94–104 | DOI | MR | Zbl

[9] Moussai M., “Composition operators on Besov algebras”, Rev. Mat. Iberoam., 28 (2012), 239–272 | DOI | MR | Zbl

[10] Moussai M., “Realizations of homogeneous Besov and Triebel-Lizorkin spaces and an application to pointwise multipliers”, Anal. Appl. (Singap.), 13:2 (2015), 149–183 | DOI | MR | Zbl

[11] Peetre J., New Thoughts on Besov Spaces, Duke Univ. Math. Series I, Durham, N.C., 1976 | MR

[12] Runst T., Sickel W., Sobolev Spaces of Fractional Order, Nemytskij Operators, and Nonlinear Partial Differential Equations, de Gruyter, Berlin, 1996 | DOI | MR | Zbl

[13] Treves F., Topological Vector Spaces, Distributions and Kernels, Academic Press, Inc., 1967 | MR | Zbl

[14] Triebel H., Theory of Function Spaces, Monogr. Math., 78, Birkhäuser, Basel, 1983 | DOI | MR | Zbl

[15] Triebel H., Theory of Function Spaces II, Monogr. Math., 84, Birkhäuser, Basel, 1992 | DOI | MR | Zbl

[16] Yamazaki M., “A quasi-homogeneous version of paradifferential operators, I. Boundedness on spaces of Besov type”, J. Fac. Sci. Univ. Tokyo, Sect. IA Math., 33 (1986), 131–174 | MR | Zbl

[17] Yuan W., Sickel W., Yang D., Morrey and Campanato Meet Besov, Lizorkin and Triebel, Lecture Notes in Mathematics, 2005, Springer, Berlin, 2010 | DOI | MR | Zbl