Voir la notice de l'article provenant de la source Math-Net.Ru
@article{AA_2018_30_2_a3, author = {A. A. Belyaev and A. A. Shkalikov}, title = {Multipliers in {Bessel} potential spaces: the case of smoothness indices of different sign}, journal = {Algebra i analiz}, pages = {76--96}, publisher = {mathdoc}, volume = {30}, number = {2}, year = {2018}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/AA_2018_30_2_a3/} }
TY - JOUR AU - A. A. Belyaev AU - A. A. Shkalikov TI - Multipliers in Bessel potential spaces: the case of smoothness indices of different sign JO - Algebra i analiz PY - 2018 SP - 76 EP - 96 VL - 30 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/AA_2018_30_2_a3/ LA - ru ID - AA_2018_30_2_a3 ER -
A. A. Belyaev; A. A. Shkalikov. Multipliers in Bessel potential spaces: the case of smoothness indices of different sign. Algebra i analiz, Tome 30 (2018) no. 2, pp. 76-96. http://geodesic.mathdoc.fr/item/AA_2018_30_2_a3/
[1] Bak Dzh. G., Shkalikov A. A., “Multiplikatory v dualnykh sobolevskikh prostranstvakh i operatory Shrëdingera s potentsialami-raspredeleniyami”, Mat. zametki, 71:5 (2002), 643–651 | DOI | MR | Zbl
[2] Belyaev A. A., Shkalikov A. A., “Multiplikatory v prostranstvakh besselevykh potentsialov: sluchai indeksov neotritsatelnoi gladkosti”, Mat. zametki, 102:5 (2017), 684–699 | DOI | MR
[3] Belyaev A. A., “Characterization of spaces of multipliers for Bessel potential spaces”, Math. Notes, 96:5 (2014), 634–646 | DOI | MR
[4] Bourdaud G., “Localisations des espaces de Besov”, Studia Math., 90:2 (1988), 153–163 | DOI | MR
[5] 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 | MR
[6] Gala S., Lemarie-Rieusset P. G., “Multipliers between Sobolev spaces and fractional differentiation”, J. Math. Anal. Appl., 322:2 (2006), 1030–1054 | DOI | MR
[7] Germain P., “Multipliers, para-multipliers and weak-strong uniqueness for the Navier–Stokes equation”, J. Differential Equations, 226:2 (2006), 373–428 | DOI | MR
[8] Kusainova L. K., Myrzagalieva A. Kh., Sultanaev Ya. T., “Ob ogranichennosti operatora Shrëdingera v vesovykh prostranstvakh Soboleva”, Mat. zametki, 99:6 (2016), 945–949 | DOI | MR
[9] Maz'ya V. G., Shaposhnikova T. O., “Characterization of multipliers in pairs of Besov spaces”, Operator theoretical methods and applications to mathematical Physics, Oper. Theory Adv. Appl., 147, Birkhaüser, Basel, 2004, 365–387 | MR
[10] Maz'ya V. G., Shaposhnikova T. O., Theory of Sobolev multipliers with applications to differential and integral operators, Grundlehren Math. Wiss., 337, Springer-Verlag, Berlin, 2009 | MR
[11] Maz'ya V. G., Verbitsky I. E., “The Schrödinger operator on the energy space: boundedness and compactness criteria”, Acta Math., 188:2 (2002), 263–302 | DOI | MR
[12] Maz'ya V. G., Verbitsky I. E., “The form boundedness criterion for the relativistic Schrödinger operator”, Ann. Inst. Fourier (Grenoble), 54:2 (2004), 317–339 | DOI | MR
[13] McLean W., Strongly elliptic systems and boundary integral equations, Cambridge Univ. Press, Cambridge, 2000 | MR
[14] Neiman-Zade M. I., Shkalikov A. A., “Operatory Shrëdingera s singulyarnymi potentsialami iz prostranstv multiplikatorov”, Mat. zametki, 66:5 (1999), 723–733 | DOI | MR | Zbl
[15] Neiman-Zade M. I., Shkalikov A. A., “Strongly elliptic operators with singular coefficients”, Russ. J. Math. Phys., 13:1 (2006), 70–78 | DOI | MR
[16] Runst T., Sickel W., Sobolev spaces of fractional order, Nemytskij operators and nonlinear partial differential equations, De Gruyter Ser. Nonlinear Anal. Appl., 3, Walter de Gruyter Co., Berlin, 1996 | MR
[17] Sickel W., “On pointwise multipliers for $F^s_{p,q}(\mathbb R^n)$ in case $\sigma_{p,q}\frac np$”, Ann. Mat. Pura Appl. (4), 176 (1999), 209–250 | DOI | MR
[18] Sickel W., Smirnov I., Localization properties of Besov spaces and of its associated multiplier spaces, Jenaer Schriften Math. Inf., Jena, 1999
[19] Sickel W., Triebel H., “Hölder inequalities and sharp embeddings in function spaces of $B^s_{p,q}$ and $F^s_{p,q}$ type”, Z. Anal. Anwend., 14:1 (1995), 105–140 | DOI | MR
[20] Strichartz R. S., “Multipliers on fractional Sobolev spaces”, J. Math. Mech., 16 (1967), 1031–1060 | MR
[21] Tribel Kh., Teoriya interpolyatsii, funktsionalnye prostranstva, differentsialnye operatory, Mir, M., 1980 | MR