We investigate compact composition operators on ceratin Lipschitzspaces of analytic functions on the closed unit disc of the plane.Our approach also leads to some results about compositionoperators on Zygmund type spaces.

In global seismology Earth’s properties of fractal nature occur. Zygmund classes appear as the most appropriate and systematic way to measure this local fractality. For the purpose of seismic wave propagation, we model the Earth’s properties as Colombeau generalized functions. In one spatial dimension, we have a precise characterization of Zygmund regularity in Colombeau algebras. This is made ...

Abstract In this paper, we study the Sobolev regularity of solutions to nonlinear second order elliptic equations with super-linear first-order terms on Riemannian manifolds, complemented Neumann boundary conditions, when source term equation belongs a Lebesgue space, under various integrability regimes. Our method is based an integral refinement Bochner identity, and leads “semilinear Calderón...

A well-known theorem of Zygmund (6) states that if n 1 < n 2 <. .. is a sequence of integers satisfying a (1) n~ +i/n~ > l+c (c > 0), k=1 converges for at least one x ; in fact the set of x for which (2) converges is of power c in any interval. Paley and Mary Weiss (5) extended this theorem for power series, i .e. (3) Y a i.znk k=1 converges for at least one z with I z I = 1 ; in fact the set o...

In this paper we show that if the real line R is not a union of less than continuum many of its meager subsets then there exists an almost continuous Sierpiński–Zygmund function having a perfect road at each point. We also prove that it is consistent with ZFC that every Darboux function f :R→ R is continuous on some set of cardinality continuum. In particular, both these results imply that the ...

Vector-valued L p-convergence of orthogonal series and Lagrange interpolation. Abstract We give necessary and sufficient conditions for interpolation inequalities of the type considered by Marcinkiewicz and Zygmund to be true in the case of Banach space-valued polynomials and Jacobi weights and nodes. We also study the vector-valued expansion problem of L p-functions in terms of Jacobi polynomi...

Consider a sequence of independent random elements {Vn, n > in a real separable normed linear space (assumed to be a Banach space in most of the results), and sequences of constants {a,, n > and {ha, n with 0 < b, "[" oo. Sets of conditions are provided for {an(V EVn) n > to obey a general strong law of large numbers of the form aj(Vj EVj)/bn --> 0 almost certainly. The hypotheses involve the d...

In this paper, we study the boundedness of pseudo-differential operators with symbols in Sm ρ,δ on the modulation spaces M p,q. We discuss the order m for the boundedness Op(Sm ρ,δ) ⊂ L(M p,q(Rn)) to be true. We also prove the existence of a Calderón-Zygmund operator which is not bounded on the modulation space Mp,q with q 6= 2. This unboundedness is still true even if we assume a generalized T...

We find a remarkably simple relationship between the following two models of the tangent space to the Universal Teichmüller Space : (1) The real-analytic model consisting of Zygmund class vector fields on the unit circle; (2) The complex-analytic model comprising 1-parameter families of schlicht functions on the exterior of the unit disc which allow quasiconformal extension. Indeed, the Fourier...

In this paper we consider the Spanne type boundedness of sublinear operators and prove the Adams type boundedness theorems for these operators and also give BMO (bounded mean oscillation space) estimates for their commutators in generalized Morrey spaces on Heisenberg groups. The boundedness conditions are formulated in terms of Zygmund type integral inequalities. Based on the properties of the...