General fractional derivatives and the Bergman projection

The Bergman Projection on Sectorial Domains

General Multiple Opial-type Inequalities for the Canavati Fractional Derivatives

In this paper we establish some general multiple Opial-type inequalities involving the Canavati fractional derivatives. In some cases the best possible constants are discussed. 1 Faculty of Civil Engineering, Architecture and Geodesy, University of Split, Split, Croatia. E-mail address: [email protected] 2 Faculty of Textile Technology, University of Zagreb, Zagreb, Croatia. E-mail address:...

Analytic Functionals and the Bergman Projection on Circular Domains

A property of the Bergman projection associated to a bounded circular domain containing the origin in C^ is proved: Functions which extend to be holomorphic in large neighborhoods of the origin are characterized as Bergman projections of smooth functions with small support near the origin. For certain circular domains D, it is also shown that functions which extend holomorphically to a neighbor...

The Bergman Kernel and Projection on Non-smooth Worm Domains

We study the Bergman kernel and projection on the worm domains Dβ = { ζ ∈ C : Re ( ζ1e −i log |ζ2| 2) > 0, ∣∣ log |ζ2| ∣∣ < β − π 2 } and D β = { z ∈ C : ∣Im z1 − log |z2| ∣∣ < π 2 , | log |z2| | < β − π 2 } for β > π. These two domains are biholomorphically equivalent via the mapping D β ∋ (z1, z2) 7→ (e z1 , z2) ∋ Dβ . We calculate the kernels explicitly, up to an error term that can be contr...

Fractional Coins and Fractional Derivatives

and Applied Analysis 3 Differential calculus Exponent