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Preconditioned Accelerated Gradient Descent Methods for Locally Lipschitz Smooth Objectives with Applications to the Solution of Nonlinear PDEs
We develop a theoretical foundation for the application of Nesterovâs accelerated gradient descent method (AGD) to the approximation of solutions of...
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Finitely bi-Lipschitz homeomorphisms between Finsler manifolds
In this paper we investigate the boundary behavior of finitely bi-Lipschitz homeomorphisms between Finsler manifolds. Our study involves the module...
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An Ay-LĂȘ-Jost-Schwachhöfer Type Characterization of Quantitatively Weakly Sufficient Statistics
We explain the notion of a \(\delta \) -almost sufficient statistic, which...
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On the characterization of harmonic functions with initial data in Morrey space
Let ( X, d, ÎŒ ) be a metric measure space satisfying the doubling condition and an L 2 -PoincarĂ© inequality. Consider the nonnegative operator
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Lipschitz Continuity of Convex Functions
We provide some necessary and sufficient conditions for a proper lower semicontinuous convex function, defined on a real Banach space, to be locally...
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Estimates for Lipschitz and BMO Norms of Operators on Differential Forms
In this paper, we introduce the generalized Lipschitz and BMO norms of differential forms and establish the upper bound estimates for the generalized...
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On Regularization by a Small Noise of Multidimensional Odes with Non-Lipschitz Coefficients
We solve a selection problem for multidimensional SDE dX ( t ) = a ( X đ ( t )) dt + đ Ï ( X đ ( t )) dW ( t ) , where the drift and diffusion are locally Lipschitz...
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A remake of BourgainâBrezisâMironescu characterization of Sobolev spaces
We introduce a large class of concentrated p -LĂ©vy integrable functions approximating the unity, which serves as the core tool from which we provide a...
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A Modulus of Smoothness for Some Banach Function Spaces
Based on the Steklov operator, we consider a modulus of smoothness for functions in some Banach function spaces, which can be not translation...
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Maximal metric surfaces and the Sobolev-to-Lipschitz property
We find maximal representatives within equivalence classes of metric spheres. For Ahlfors regular spheres these are uniquely characterized by...
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Lipschitz Type Characterizations for Bergman-Orlicz Spaces and Their Applications
We give characterizations for Bergman-Orlicz spaces with standard weights via a Lipschitz type condition in the Euclidean, hyperbolic, and...
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Asymptotic Estimates for the Growth of Deformed Hankel Transform by Modulus of Continuity
We derive asymptotic estimates for the growth of the norm of the deformed Hankel transform on the deformed HankelâLipschitz space defined via a...
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Projectional Coderivatives and Calculus Rules
This paper is devoted to the study of a newly introduced tool, projectional coderivatives, and the corresponding calculus rules in finite dimensional...
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Boundedness of multi-parameter pseudo-differential operators on multi-parameter Lipschitz spaces
The main purpose of this paper is to introduce the multi-parameter Lipschitz spaces and characterize it via the LittlewoodâPaley theory. As an...
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Generalized Composition Operators from the Lipschitz Space into the Zygmund Space
AbstractIn this paper, at first we study boundedness and compactness criterions for generalized composition operator from the Lipschitz space into...