Notes on best constants in some Sobolev inequalities

, . .     

Some expansion formulae for Fox'sH-function of two variables involving associated Legendre functions

H- .     

On the newly generalized absolute Riesz summability of orthogonal series

[3] , [1], ¦C,,(t)¦ _k - . , , ¦R, , (t)¦ _k - ¦R, , (t)¦ _k - . (t)=1,k=1 [7], [9].

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This research was partially supported by the Hungarian National Foundation for Scientific Research under Grant#T 016 393.     

On equivalence of rearrangements of the Haar system in dyadic Hardy and BMO spaces

H={h ₁,I } — , . : , I ¦(I)¦=¦I¦, ¦I¦ — I. H H ={h _(I),I} . , , . L ^p .

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Dedicated to Professor B. Szökefalvi-Nagy on his 75th birthday

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This research was supported in part by MTA-NSF Grants INT-8400708 and 8620153.     

On convergence of multiparameter strong submartingales in Banach lattices

- , ., B - — , B- {M _n ,nN ^d } n. .     

Rate of approximation by rectangular partial sums of double orthogonal series

( ) . .

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Dedicated to Professor K. Tandori on his seventieth birthday

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This research was supported in part by Grant # K41 100 of the Joint Fund of the Government of Ukraine and the International Science Foundation.     

Fibred links and a construction of real singularities via complex geometry

This note gives a method for constructing real analytic maps from ²ⁿ into ², with an isolated critical point at 0 ²ⁿ , for alln>1. This provides infinite families of real singularities which fiber a la Milnor.Research partially supported by CONACYT, Mexico, grant 1206-E92103.     

Topology of Definable Hausdorff Limits

Let A ^n+r be a set definable in an o-minimal expansion S of the real field, let A ^r be its projection, and assume that the non-empty fibers A_a ⁿ are compact for all a A and uniformly bounded, i.e. all fibers are contained in a ball of fixed radius B(0,R). If L is the Hausdorff limit of a sequence of fibers A_ai, we give an upper-bound for the Betti numbers b_k(L) in terms of definable sets explicitly constructed from a fiber A_a. In particular, this allows us to establish effective complexity bounds in the semialgebraic case and in the Pfaffian case. In the Pfaffian setting, Gabrielov introduced the relative closure to construct the o-minimal structure S_Pfaff generated by Pfaffian functions in a way that is adapted to complexity problems. Our results can be used to estimate the Betti numbers of a relative closure (X,Y)₀ in the special case where Y=.     

On rearrangements of orthogonal sets

{ _d } , c _{n n} (x) , {c _n }l ². () . , .. 1) ()< { _n} — , {_(n)} m .2) ()=, {_n {c_n}l ² , c _{n (n)} . , { _n } .     

Eine Bemerkung zu den höheren Pythagoraszahlen reeller Körper

Becker has shown in [1] that for the 4-th Pythagoras number of the field (X) the inequality P₄ ((X)) 36 holds. In this paper we will show P₄ ((X)) 24 and P₄ (K) 3 for all real pythagorean fields K.     

Markuševič decompositions and quasireflexivity of Banach spaces

. , , . .     

Interpolation and best polynomial approximation in the domain ofp-adic integers

, , . , . Lip

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The authors are indebted to Professor R. Bojanic for his valuable remarks and suggestions, especially for the simplification of the proof of Theorem 4.     

Hardy spaces of predictable martingales

, P _p Q _p .

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This research was partially supported by the Hungarian Scientific Foundation.     

Achtdimensionale lokalkompakte Translationsebenen mit großen kompakten Kollineationsgruppen

This paper is part of a program aiming at the classification of all higher-dimensional locally compact translation planes whose collineation groups have large dimension. In the present paper we determine all eight-dimensional locally compact translation planes which admit acompact collineation group of dimension at least 5 acting almost effectively on the translation axis. In fact, is isomorphic either to Spin₄ or toSO ₄(). The case Spin₄() has already been treated elsewhere ([6]). Here, the planes with SO ₄() are explicitly determined and studied in detail.     

A refinement of an estimate of the arithmetic minimum of the product of nonhomogeneous linear forms (regarding Minkowski's nonhomogeneous conjecture)

One refines an estimate of B. F. Skubenko (Tr. Mat. Inst. Akad. Nauk 148, 218–224 (1978)). Let be a point lattice of determinant d() in the n-dimensional Euclidean space ⁿ. and let L^ñ. We consider the nonhomogeneous One proves that there exists an effectively computable constant n_o such that if nn_o, then.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 82, pp. 88–94, 1979.     

A generalization of the Heine limit for functions which converge on a base

. , , . . . .     

Оъ одной Задаче из Теории Процессов Размножения и Гибели

. [4].      

Inequalities for upper bounds of functionals

. . . , , .     

Mapping properties of non-linear operators in spaces of Triebel-Lizorkin and Besov type

— . - G , G: f G(f) _p,q ^s (R_n) F _p,q ^s (R_n).     

On the domain dependence of solutions to the two-phase Stefan problem

We prove that solutions to the two-phase Stefan problem defined on a sequence of spatial domains _n ^N converge to a solution of the same problem on a domain where is the limit of _n in the sense of Mosco. The corresponding free boundaries converge in the sense of Lebesgue measure on ^N.