A compactness result of Janson type for bilinear operators

We establish a compactness interpolation result for bilinear operators of the type proved by Janson for bounded bilinear operators. We also give an application to compactness of convolution operators.

[1]  J. Peetre,et al.  Interpolation of compactness using Aronszajn-Gagliardo functors , 1989 .

[2]  A. Persson.  Compact linear mappings between interpolation spaces , 1964 .

[3]  Fernando Cobos,et al.  Interpolation of the measure of non-compactness of bilinear operators among quasi-Banach spaces , 2019, J. Approx. Theory.

[4]  Joseph Kupka,et al.  $L_{p,q}$ spaces , 1980 .

[5]  J. Lions,et al.  Sur Une Classe D’Espaces D’Interpolation , 1964 .

[6]  H. Triebel,et al.  Über die Verteilung der Approximationszahlen kompakter Operatoren in Sobolev-Besov-Räumen , 1967 .

[7]  F. Cobos,et al.  Interpolation of compact bilinear operators among quasi‐Banach spaces and applications , 2018 .

[8]  A. Calderón.  Intermediate spaces and interpolation, the complex method , 1964 .

[9]  D. Edmunds,et al.  Interpolation theory and measures of non‐compactness , 1981 .

[10]  C. Thiele.  Interpolation of multilinear operators , 2006 .

[11]  L. M. Fernández-Cabrera,et al.  Real Interpolation of Compact Bilinear Operators , 2018 .

[12]  F. Cobos,et al.  On compactness results of Lions–Peetre type for bilinear operators , 2020 .

[13]  Á. Bényi,et al.  Smoothing of commutators for a H\"ormander class of bilinear pseudodifferential operators , 2013, 1305.4307.

[14]  M. Mastyło,et al.  Interpolation of the measure of noncompactness of bilinear operators , 2017, Transactions of the American Mathematical Society.

[15]  Á. Bényi,et al.  Compact Bilinear Operators and Commutators , 2013 .

[16]  H. König.  Interpolation of operator ideals with an application to eigenvalue distribution problems , 1978 .

[17]  Richard O’Neil,et al.  Convolution operators and $L(p,q)$ spaces , 1963 .

[18]  On Schauder bases in the Lorentz operator ideal , 1983 .

[19]  L. M. Fernández‐Cabrera,et al.  On interpolation properties of compact bilinear operators , 2017 .

[20]  T. Kühn,et al.  One-sided compactness results for Aronszajn-Gagliardo functors , 1992 .

[21]  D. L. Fernandez,et al.  Interpolation of bilinear operators and compactness , 2010, 1206.0017.