Let $$\Omega \subset {\mathbb {C}}^n$$ be a smooth bounded pseudoconvex domain and $$A^2 (\Omega )$$ denote its Bergman space. $$P:L^2(\Omega )\longrightarrow A^2(\Omega the projection. For measurable $$\varphi :\Omega \longrightarrow \Omega $$ , projected composition operator is defined by $$(K_\varphi f)(z) = P(f \circ \varphi )(z), z \in f\in A^2 ).$$ In 1994, Rochberg studied boundedness of...

We provide a boundedness criterion for the integral operator $$S_{\varphi }$$ on fractional Fock–Sobolev space $$F^{s,2}({{\mathbb {C}}}^n)$$ , $$s\ge 0$$ where (introduced by Zhu [18]) is given $$\begin{aligned} S_{\varphi }F(z):= \int _{{\mathbb {C}}^n} F(w) e^{z \cdot \bar{w}} \varphi (z- \bar{w}) d\lambda (w) \end{aligned}$$ with $$\varphi $$ in Fock $$F^2({{\mathbb {C}}^n})$$ and $$d\lambd...

‎In this paper‎, ‎we introduce more general contractions called $varphi $-fixed‎ ‎point point for $(F,varphi‎ ,‎alpha )_{s}$ and $(F,varphi‎ ,‎alpha )_{s}$-‎weak contractions‎. ‎We prove the existence and uniqueness of $varphi $-‎fixed point point for $(F,varphi‎ ,‎alpha )_{s}$ and $(F,varphi‎ ,‎alpha‎‎)_{s}$-weak contractions in complete $b$-metric spaces‎. ‎Some examples are‎ ‎supplied to sup...

In this paper we define $varphi$-Connes module amenability of a dual Banach algebra $mathcal{A}$ where $varphi$ is a bounded $w_{k^*}$-module homomorphism from $mathcal{A}$ to $mathcal{A}$. We are mainly concerned with the study of $varphi$-module normal virtual diagonals. We show that if $S$ is a weakly cancellative inverse semigroup with subsemigroup $E$ of idemp...

The Kodaira-Spencer map is a component of the connection ∇. In particular, this implies that if κs 6= 0 then the connection∇ is nontrivial with respect to the Hodge decomposition. Various Hodge-theory facts imply that the global monodromy must be nontrivial in this case. We can be a bit more precise: if u ∈ V p,q is a vector such that κs(v)(u) 6= 0 for some tangent vector v ∈ T (S)s, then u can...

in this paper, a commutative semigroup will be written as a disjoint :union: of its cancellative subsemigroups. based on this fact we will define the left regular representation of a commutative separative semigroup and show that this representation is faithful. finally concrete examples of commutative separative semigroups, their decompositions and their left regular representations are given.

in this paper, we define the notions of fuzzy congruence relations and fuzzy convex subalgebras on a commutative residuated lattice and we obtain some related results. in particular, we will show that there exists a one to one correspondence between the set of all fuzzy congruence relations and the set of all fuzzy convex subalgebras on a commutative residuated lattice. then we study fuzzy...

In this paper, we define the notions of fuzzy congruence relations and fuzzy convex subalgebras on a commutative residuated lattice and we obtain some related results. In particular, we will show that there exists a one to one correspondence between the set of all fuzzy congruence relations and the set of all fuzzy convex subalgebras on a commutative residuated lattice. Then we study fuzzy...