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We give some explicit values of the constants $C_{1}$ and $C_{2}$ in the inequality $C_{1} / sin (\frac{π}{p}) \leq {|P|}_{p} \leq C_{2} / sin (\frac{π}{p})$ where ${|P|}_{p}$ denotes the norm of the Bergman projection on the $L^{p}$ space.

Exact asymptotic behavior of singular values of a class of integral operators

Milutin R. Dostanić — 1999

Czechoslovak Mathematical Journal

We find an exact asymptotic formula for the singular values of the integral operator of the form $\int_{Ω} T (x, y) k (x - y) \cdot d y L^{2} (Ω) \to L^{2} (Ω)$ ( $Ω \subset ℝ^{m}$ , a Jordan measurable set) where $k (t) = k_{0} ({(t_{1}^{2} + t_{2}^{2} + ... t_{m}^{2})}^{\frac{m}{2}})$ , $k_{0} (x) = x^{α - 1} L (\frac{1}{x})$ , $\frac{1}{2} - \frac{1}{2 m} < α < \frac{1}{2}$ and $L$ is slowly varying function with some additional properties. The formula is an explicit expression in terms of $L$ and $T$ .

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Boundedness of the Bergman projections of $L^{p}$ spaces with radial weights

Some Estimations of Positive and Negative Eigenvalues for an Inhomogeneous Membrane

On a Theorem of Ky-Fan Type

Trace Formulas of Gelfand--levitan Type

Generalization of the Mercer Theorem

Asymptotic Behavior of Eigenvalues of Certain Integral Operators

Trace Formula for Nonnuclear Perturbations of Selfađoint Operators

Generalized Eigenvector Expansion for Weakly Perturbated Discrete Operators

Spectral Properties of the Cauchy Operator and the Operator of Logarithmic Potential Type on L2 Space With Radial Weight

Bilinear Expansions of the Kernels of Some Nonselfadjoint Integral Operators

On the Expansion Theorem for a Certain Boundary Value Problem for a Functional Differential Equation

Some Estimates of the Remainder in the Expressions for the Eigenvalue Asymptotics of Some Singular Integral Operators

Exact Asymptotic Behaviour of the Singular Values of Integral Operators With the Kernel Having Singularity on the Diagonal

The Regularized Trace for Nuclear Perturbations of Discrete Operators

Two sided norm estimate of the Bergman projection on $L^{p}$ spaces

Exact asymptotic behavior of singular values of a class of integral operators

Bilinear expansions of the kernels of some nonselfadjoint integral operators.

A basis property of families of the Mittag-Leffler functions.

Some inequalities for entire functions of exponential type.

Inequality of Poincaré-Friedrich's type on $L^{p}$ spaces.