In this paper, we study the following operator equation: p ∈ Ax + Cx in a Banach space X , where A : D(A) ⊆ X → 2X is an accretive mapping, C : D(C) ⊆ X → X is a nonlinear mapping and p ∈ X . Various existence results of solutions of nonlinear operator equations in Banach spaces are obtained under a countably condensing type condition. © 2004 Elsevier Ltd. All rights reserved.

For the iteration of spherical average (A1)N and Laplace operator Δ, we consider boundedness Δ(A1)N on α-modulation spaces \(M_{p,q}^{s,\alpha }\). The authors obtain some sufficient necessary conditions to ensure spaces. main theorems significantly improve known results.

In this paper, first we give a notion for linear Weingarten spacelike hypersurfaces with P + aH = b in a locally symmetric Lorentz space Ln+1 1 . Furthermore, we study complete or compact linear Weingarten spacelike hypersurfaces in locally symmetric Lorentz spaces Ln+1 1 satisfying some curvature conditions. By modifying Cheng-Yau’s operator given in [7], we introduce a modified operator L and...

It is well known that the Hilbert tranformation and the conjugate function operator restricted to even (odd) functions define bounded linear operators on weighted If spaces under more general conditions than is the case for the unrestricted operators. In analogy with recent results of Hunt, Muckenhoupt and Wheeden for the Hilbert transform and the conjugate function operator, we obtain necessar...

The notions of column and row operator space were extended by A. Lambert from Hilbert spaces to general Banach spaces. In this paper, we use column and row spaces over quotients of subspaces of general Lp-spaces to equip several Banach algebras occurring naturally in abstract harmonic analysis with canonical, yet not obvious operator space structures that turn them into completely bounded Banac...

We prove that, under a mild condition on couple (A0,A1) of quasi-Banach spaces, all real interpolation spaces (A0,A1)?,p with 0<?<1 and 0<p?? are different from each other. In the Banach case for 1?p?? this was shown by Janson, Nilsson, Peetre Zafran, thus solving an old problem posed J.-L. Lions. Moreover, we give application to certain which important objects in Operator Theory consist bounde...