In this paper,we investigate Sobolev mapping properties of the Bergman projection.Th domain we focus on is defined byΩm/n:={(z,w)∈C^(1+N):|w1|<|z|m1/n1<1,…|wN|<|z|/m_(N)/n_(N)<1},where m=(m1,…mN)∈(Z^(+))^(N),n=(n1,…nN)∈(Z^(+))N,N∈Z^(+).Sobolev irregularity of the Bergman projections on 2 is shown.We also prove some Sobolev regularity results of the Bergman projections onΩm/n for m=(1,…1).
We consider dual Toeplitz operators on the orthogonal complements of the FockSobolev spaces of all nonnegative real orders.First,for symbols in a certain class containing all bounded functions,we study the problem of when an operator which is finite sums of the dual Toeplitz products is compact or zero.Next,for bounded symbols,we construct a symbol map and exhibit a short exact sequence associated with the C^(*)-algebra generated by all dual Toeplitz operators with bounded symbols.
In this paper,we firstly recall some basic results on pseudo S-asymptotically(ω,c)-periodic functions and Sobolev type fractional differential equation.We secondly investigate some existence of pseudo S-asymptotically(ω,c)-periodic solutions for a semilinear fractional differential equations of Sobolev type.We finally present a simple example.
