Proposition 4.1(i) of [1] is incorrect, i.e. the sequence of Cesàro-sections of a sequence x in a translation invariant BK-space is not necessarily bounded. Theorem 4.2(ii) of [1] and the proof of Proposition 4.3 of [1] are corrected. All other statements of [1], including Proposition 4.3 itself, are correct.
We provide a modification for part of the proof of Theorem 1.2 of our article, pages 85-89, under the multivariable T(1) cancellation condition.
The following result is proved: to give two consecutive polynomials , of an orthonormal system is equivalent to assign the first moments of the Lebesgue-Stieltjes measure associated with the system.
Étant donné une courbe de Jordan rectifiable du plan complexe admettant le paramétrage par la longueur d’arc , on étudie les relations entre la géométrie de et la position dans des deux espaces de Hardy associés à . Plus précisément, on montre que si est la somme presque-orthogonale des espaces de Hardy, la courbe satisfait à une condition de type corde-arc, c’est-à-dire que pour tout et tout de , . Ce résultat est une sorte de réciproque à la généralisation du théorème de Calderón...
We are concerned with imbeddings of general spaces of Besov and Lizorkin-Triebel type with dominating mixed derivatives in the first critical case. We employ multivariate exponential Orlicz and Lorentz-Orlicz spaces as targets. We study basic properties of the target spaces, in particular, we compare them with usual exponential spaces, showing that in this case the multivariate clones are in fact better adapted to the character of smoothness of the imbedded spaces. Then we prove sharp limiting imbedding...
In a recent paper [3] C. Baiocchi, V. Komornik and P. Loreti obtained a generalisation of Parseval's identity by means of divided differences. We give here a proof of the optimality of that theorem.
Our primary goal in this preamble is to highlight the best of Vasil Popov’s mathematical achievements and ideas. V. Popov showed his extraordinary talent for mathematics in his early papers in the (typically Bulgarian) area of approximation in the Hausdorff metric. His results in this area are very well presented in the monograph of his advisor Bl. Sendov, “Hausdorff Approximation”.