scholarly journals Calderón's Problem for Lipschitz Classes and the Dimension of Quasicircles

1988 ◽  
pp. 469-486 ◽  
Author(s):  
Kari Astala
Keyword(s):  
Lipschitz Classes

scholarly journals Quantitative Estimates for Nonlinear Sampling Kantorovich Operators

2021 ◽  
Vol 76 (2) ◽  
Author(s):  
Nursel Çetin ◽  
Danilo Costarelli ◽  
Gianluca Vinti
Keyword(s):  
Orlicz Spaces ◽  
General Setting ◽  
Modulus Of Smoothness ◽  
Direct Approach ◽  
Order Of Approximation ◽  
Lipschitz Classes ◽  
General Frame ◽  
Quantitative Estimates ◽  
Nonlinear Sampling ◽  
Kantorovich Operators

AbstractIn this paper, we establish quantitative estimates for nonlinear sampling Kantorovich operators in terms of the modulus of smoothness in the setting of Orlicz spaces. This general frame allows us to directly deduce some quantitative estimates of approximation in $$L^{p}$$ L p -spaces, $$1\le p<\infty $$ 1 ≤ p < ∞ , and in other well-known instances of Orlicz spaces, such as the Zygmung and the exponential spaces. Further, the qualitative order of approximation has been obtained assuming f in suitable Lipschitz classes. The above estimates achieved in the general setting of Orlicz spaces, have been also improved in the $$L^p$$ L p -case, using a direct approach suitable to this context. At the end, we consider the particular cases of the nonlinear sampling Kantorovich operators constructed by using some special kernels.

On approximation in Weighted Orlicz spaces

2012 ◽  
Vol 62 (1) ◽  
Author(s):  
Ali Guven ◽  
Daniyal Israfilov
Keyword(s):  
Approximation Theory ◽  
Orlicz Spaces ◽  
Trigonometric Approximation ◽  
Inverse Theorem ◽  
Lipschitz Classes

AbstractAn inverse theorem of the trigonometric approximation theory in Weighted Orlicz spaces is proved and the constructive characterization of the generalized Lipschitz classes defined in these spaces is obtained.

scholarly journals On Jordan ARCS and Lipschitz classes of functions defined on them

1961 ◽  
Vol 106 (1-2) ◽  
pp. 113-136 ◽  
Author(s):  
A. S. Besicovitch ◽  
I. J. Schoenberg
Keyword(s):  
Lipschitz Classes ◽  
Jordan Arcs
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