
doi: 10.1007/bf01388419
Let \(\psi\in L^ 2(\mathbb{R}^ d)\) be an admissible wavelet, \(\psi_ \xi(x)= t^{-d/2} \psi\Bigl({x-v\over t}\Bigr)\), \(\xi= (v,t)\), \(G\) the ``\(ax+ b\)''-group, i.e. \(G=\{\xi= (v,t): v\in \mathbb{R}^ d, t>0\}\), \(d\xi= t^{d-1}dv dt\) the left invariant measure on \(G\). For a Borel measure \(\mu\) on \(G\), for which \[ {\mathcal D}(T_ \mu)= \left\{f\in L_ 2(\mathbb{R}^ d): \int_ G |\langle f,\psi_ \xi\rangle|^ 2 d|\mu|<\infty\right\} \] is dense in \(L^ 2(\mathbb{R}^ d)\), a Calderón-Toeplitz operator is defined by the formula \[ \langle T_ \mu f,g\rangle= \int_ G \langle f,\psi_ \xi\rangle\langle\psi_ \xi,g\rangle d\mu, \] where \(f,g\in {\mathcal D}(T_ \mu)\). Calderón-Toeplitz operators are connected with Calderón-Zygmund operators. On the other hand these operators generalize Toeplitz operators defined on weight Bergman spaces on the upper half plane. The author discusses boundness and Schatten ideal criteria for a class Calderón-Toeplitz operators.
Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.), left invariant measure, admissible wavelet, Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, Calderón-Zygmund operators, boundness, Schatten ideal, General harmonic expansions, frames, singular numbers, Article, Borel measure, Calderón-Toeplitz operator, 510.mathematics, Toeplitz operators, Hankel operators, Wiener-Hopf operators, Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
Linear operators belonging to operator ideals (nuclear, \(p\)-summing, in the Schatten-von Neumann classes, etc.), left invariant measure, admissible wavelet, Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, Calderón-Zygmund operators, boundness, Schatten ideal, General harmonic expansions, frames, singular numbers, Article, Borel measure, Calderón-Toeplitz operator, 510.mathematics, Toeplitz operators, Hankel operators, Wiener-Hopf operators, Riesz operators; eigenvalue distributions; approximation numbers, \(s\)-numbers, Kolmogorov numbers, entropy numbers, etc. of operators
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