Eigenvalue distribution of integral operators defined by Besov-Orlicz kernels.
Eigenvalue distribution of integral operators defined by Orlicz kernels.
Embedding functions and their role in interpolation theory.
Embeddings of Besov spaces of logarithmic smoothness
This paper deals with Besov spaces of logarithmic smoothness formed by periodic functions. We study embeddings of into Lorentz-Zygmund spaces . Our techniques rely on the approximation structure of , Nikol’skiĭ type inequalities, extrapolation properties of and interpolation.
Endpoint estimates from restricted rearrangement inequalities.
Entropy numbers of diagonal operators of logarithmic type.
Equivalence Between K-functionals Based on Continuous Linear Transforms
2000 Mathematics Subject Classification: 46B70, 41A10, 41A25, 41A27, 41A35, 41A36, 42A10.The paper presents a method of relating two K-functionals by means of a continuous linear transform of the function. In particular, a characterization of various weighted K-functionals by unweighted fixed-step moduli of smoothness is derived. This is applied in estimating the rate of convergence of several approximation processes.Partially supported by grant No. 103/2007 of the National Science Fund of the Sofia University....
Estimates for maximal singular integrals
It is shown that maximal truncations of nonconvolution L²-bounded singular integral operators with kernels satisfying Hörmander’s condition are weak type (1,1) and -bounded for 1 < p< ∞. Under stronger smoothness conditions, such estimates can be obtained using a generalization of Cotlar’s inequality. This inequality is not applicable here and the point of this article is to treat the boundedness of such maximal singular integral operators in an alternative way.
Estimation of the position of intermediate spaces for a Banach couple
The position of intermediate spaces for a Banach couple is estimated with the help of its fundamental function and co-function. We study the completeness of the collection of all such functions, and the methods of calculating and estimating them for different couples. Finally, these functions are used to compare the position of spaces obtained under the action of some interpolation functors.
Extrapolation functors on a family of scales generated by the real interpolation method.
Extrapolatory description for the Lorentz and Marcinkiewicz spaces “close" to .
Extreme cases of weak type interpolation.
We consider quasilinear operators T of joint weak type (a, b; p, q) (in the sense of [2]) and study their properties on spaces Lφ,E with the norm||φ(t) f*(t)||Ê, where Ê is arbitrary rearrangement-invariant space with respect to the measure dt/t. A space Lφ,E is said to be "close" to one of the endpoints of interpolation if the corresponding Boyd index of this space is equal to 1/a or to 1/p. For all possible kinds of such "closeness", we give sharp estimates for the function ψ(t) so as to obtain...