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ON SOME EXTREMAL PROBLEMS IN CERTAIN HARMONIC FUNCTION SPACES OF SEVERAL VARIABLES RELATED TO MIXED NORM SPACES

R F Shamoyan
2013 Problemy Analiza  
Namely some estimates on distances in spaces of harmonic functions in the unit ball and the upper half space are provided.  ...  In this paper we provide some (not new) estimates on distances from our two previous papers together with some new estimates.  ...  This direction of investigation related to extremal problems in harmonic function spaces started in [1] , then continued in [2] , [3] .  ... 
doi:10.15393/j3.art.2013.2324 fatcat:ambqmokpsncofc6xdfxxjvzatu

On some extremal problems in certain harmonic function spaces of several variables related to mixed norm spaces [article]

Romi F.Shamoyan
2012 arXiv   pre-print
We provide some new estimates for distances in harmonic function spaces of several variables related to mixed norm spaces.Some of them extend previously known assertions in this direction in the unit ball  ...  This direction of investigation related to extremal problems in harmonic function spaces started in [1] ,then continued in [2] , [4] In this note in particular a new sharp theorem on distances in harmonic  ...  issues connected with extremal problems .  ... 
arXiv:1205.0171v1 fatcat:oherrzisnncyrkdbvt7hioz2nm

Optimal Lipschitz extensions

Thanh Viet Phan, R. Briš, Gyu Whan Chang, Chu Duc Khanh, M. Razzaghi, K. Stempak, Thanh Toan Phan
2018 ITM Web of Conferences  
The classical Lipschitz extension problem in concerned for conditions on a pair of metric spaces (X, d X ) and (Y, d Y ) such that for all Ω ⊂ X and for all Lipschitz function f : Ω → Y, then there is  ...  In this paper we discuss some results and open questions related to that issue.  ...  Kirszbraun theorem and McShane-Whitney extremal extensions It is rare for a pair of metric spaces (X, Y) to have the isometric extension property.  ... 
doi:10.1051/itmconf/20182002010 fatcat:ncjlmj2xbjhvxpoehh6ciq6evm

The February meeting of the San Francisco Section

W. A. Manning
1909 Bulletin of the American Mathematical Society  
IT is a well-known theorem of the calculus of variations,* that if all the members of a one parameter family of plane curves pass through a fixed point O, then any arc of these extremals which does not  ...  ALLARDICE. " Note on the reduction of a circulant." (3) Professor R. E. ALLARDICE. " A theorem in the partition of numbers." (4) Professor W. A. MANNING. " On the order of primitive groups.  ... 
doi:10.1090/s0002-9904-1909-01771-9 fatcat:clwtmhe5erflxkfbk7wfqszugy

The branch set of a quasiregular mapping [article]

Juha Heinonen
2003 arXiv   pre-print
Other recent progress and open problems of a more function theoretic nature are also presented.  ...  We discuss the issue of branching in quasiregular mapping, and in particular the relation between branching and the problem of finding geometric parametrizations for topological manifolds.  ...  According to a theorem of Whitney [45, Chapter IX], flat forms (ρ i ) have a well defined trace on X, and on the measurable tangent bundle of X, essentially because of the rectifiability. 5 Because  ... 
arXiv:math/0304333v1 fatcat:wbortcax7nb27accmwcvzviysu

Majorization and Rényi Entropy Inequalities via Sperner Theory [article]

Mokshay Madiman, Liyao Wang, Jae Oh Woo
2018 arXiv   pre-print
It is then used to obtain a variety of consequences, including new R\'enyi entropy inequalities for sums of independent, integer-valued random variables.  ...  A natural link between the notions of majorization and strongly Sperner posets is elucidated.  ...  Acknowledgments The authors are indebted to Manjunath Krishnapur for very useful discussions, and to two anonymous reviewers for detailed and constructive comments that greatly improved the exposition.  ... 
arXiv:1712.00913v3 fatcat:zrlub7zupbhw3ke4rqmjuropxa

Page 4418 of Mathematical Reviews Vol. , Issue 98G [page]

1998 Mathematical Reviews  
Summary: “The rounding of o-filters is introduced and this con- cept is used to construct an extremally disconnected Hausdorff reflection for a given extremally disconnected space.  ...  [Hyperspaces of sets, Dekker, New York, 1978; MR 58 #18330] for information on hyperspaces and related topics. Let u: C(X) — R denote a Whitney map from C(X) into the reals R.  ... 

Sperner families over a subset

Ko-Wei Lih
1980 Journal of combinatorial theory. Series A  
The number 1 P, j is called the mth Whitney number of P by Crapo and Rota i I]* P is said to be Sperner if max, 1 P, / = max{l A j j A is an antichain in P).  ...  A set A of elements of P is an antichain in P if two arbitrary distinct elements of A are not related by the partial order of P. Let P, denote the set of elements in P having rank m.  ... 
doi:10.1016/0097-3165(80)90007-2 fatcat:gvdxfnhgqvhajgvw3rkzne6sta

Weighted tent spaces with Whitney averages: factorization, interpolation and duality

Yi Huang
2015 Mathematische Zeitschrift  
Acknowledgement As part of the author's thesis project, the current paper is written under the guidance of Prof. Pascal Auscher, whose patience is greatly acknowledged.  ...  The author would like to thank Pascal Auscher and Henri Martikainen for helpful discussions.  ...  of [5] , where more backgrounds on boundary value problems of elliptic PDEs can be referred.  ... 
doi:10.1007/s00209-015-1570-0 fatcat:pxa7y7gysra2zpzqlpmmni2tia

Page 2999 of Mathematical Reviews Vol. , Issue 85g [page]

1985 Mathematical Reviews  
Their theorems also charac- terize the extremal arrangements.  ...  A new proof of this result is given as well as a Krasnosel'skii theorem for (d — 2)- extreme points which combines and generalizes previous results.”  ... 

Page 2082 of Mathematical Reviews Vol. 22, Issue 12A [page]

1961 Mathematical Reviews  
(Essentially, (1) is Hahn’s theorem 28.9.51 and (2) Hahn’s theorem 28.9.4.) An example of a sequence of continuous functions which converge to a continuous function, but not continuously, is given.  ...  Résolution d’un probléme de M. Z. Zahorski sur les limites approximatives. Fund. Math. 48 (1959/60), 277-286. A consequence of a theorem of W. H.  ... 

Page 7302 of Mathematical Reviews Vol. , Issue 95m [page]

1995 Mathematical Reviews  
Section 6.2 takes up the corre- sponding extremal problems on restricted classes of polynomials, while Section 6.3 deals with the extremal problems in a circle on the complex plane.  ...  norm with prescribed zeros, extremal problems in mixed norms, as well as Szeg6’s and related extremal problems. Sec- tion 5.2 treats incomplete polynomials introduced in 1976 by G. G.  ... 

Smoothness and Smooth Extensions (I): Generalization of MWK Functions and Gradually Varied Functions [article]

Li Chen
2010 arXiv   pre-print
This paper gives philosophical consideration of smoothness for practical problems, rather than a mathematical deduction or reduction, even though our inferences are based on solid mathematics.  ...  However, we do have a concept of smooth surfaces in practice since we always compare whether one surface is smoother than another one.  ...  Based on McShane-Whitney-Kirszbraun theorem, a continuous surface always exists.  ... 
arXiv:1005.3727v1 fatcat:qpg5yprgp5fh7kxfugddri4nrq

Page 2601 of Mathematical Reviews Vol. , Issue 2002D [page]

2002 Mathematical Reviews  
Summary: “We obtain a series of results related to minimiza- tion of exact constants in Jackson-type inequalities and widths in L,{0, 27].” J.  ...  Due to the Bernstein inequality, one might expect that in the last setting the extreme points for the nth Markov factor M,, i.e. such points xo € E that there is a nonzero polynomial P,, of degree <n for  ... 

Page 2633 of Mathematical Reviews Vol. , Issue 2003d [page]

2003 Mathematical Reviews  
In this paper, we use the y-q minimax transform to assign an extremal circle (dual circle) to each circle contained in the unit disk and then to prove that there exists a maximal circle which coincides  ...  2633 The authors prove the above result and related ones using a functional-analytic technique.  ... 
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