Exact estimates for partially monotone approximation

f(x) — , - [–1,1], (f, ) — , as— f, . . (- ) (x _i,x _{i+ 1}) (i=0, 1, ...,s–1; =–1,x _s,=1), f(x) . , n=0,1,... _n() , [– 1,1] signf(x) sign _n(x) 0, ¦f(x)– _n(x)¦ C(s) (f, 1/n+1, C(s) s. , - , « » .     

НАИЛУЧШЕЕ ПРИБЛИЖЕ НИЕ УГЛОМ И ПРИБЛИЖЕНИЕ УГЛОМ ИЗ СИНГУЛЯРНЫХ ИНТЕГРАЛОВ ФУНКЦИЙf∈L p (R n ),2<P<∞

. .     

Maximal inequalities,convexity inequality,and their duality. II

, , . . . [1], , . , , ., , L logL. , , . . . . [5]. , .     

О лагранжевом интерполировании с узлами в корнях многочленов сонина-маркова

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On aU-set for multiple Walsh series

m- (m2) , - , .     

Investigation of Haar and Franklin series in Hardy spaces

(L ¹,H) (, ) , ; H — . , , L ¹ . [13] , . , , , .     

On approximation of functions on the half-line by algebraic polynomials

, . , .     

О предельном распределении для сумм независимых слууайных велиуин на бикомпактных коммутативных топологиуеских группах

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On the angular derivative and univalence

f . , , — , A f f(). , , f() 0 . , , ,A , f . , f() - f() . , , . (1976) ( ¦f(z)¦<1) . . (1969) ( ).     

Extension of functions,which are traces of functions belonging to 249-01249-01249-01on an arbitrary subset of the line

( , k) , ER f(x) f(x)H _k (R) (k2— ,=(t) — k- ). f(x) E (t).     

A generalized Laplace transform of generalized functions

- . . . , .     

On approximation by Riesz means concerning orthogonal series

, , . .

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Dedicated to Academician S. M. Nikol'skii on his 90th birthday

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This research was partially supported by the Hungarian National Foundation for Scientific Research under Grant # 234.     

Замечания об ихтерполировании

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On the asymptotic distribution of oscillation points in rational approximation

. . ( ) , , (m) (m)m, n(m) ^* ) ( d(m) — r _{m, n(m)} ^*) )/ , .

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The paper was written during the second author's visit at the Mathematical Institute of the Hungarian Academy of Sciences.     

On the summability of Fourier series with the method of lacunary arithmetic means

. f- ,S _n (f)— . {n _k }, n _k+1/n _k >1+ck ^– ,— , 0<1/2, f ₀, .     

On the divergence of spherical sums of double Fourier-Haar series

. : [0, +) [0, +) - , u+ (u) (u)=o(u lnu). [0, 1]² f , ¦f¦ L([0, 1]²), - [0, 1]².     

On term by term dyadic differentiability of Walsh series

. . . . : {ja _j },j=1,2,... — , f(x) , , f ^[1](x) — f .     

Orthonormal systems satisfying an inequality of S. M. Nikol'skii

N- (p, q) (1 pN-, L _p - L _q -. , , , L L _q - , , .     

Spectral orders and convolution

. (R) _{– –} fg(y)h(x–y) dx dy _{– –} f ^{^} (x)g ^{^} (y)h ^{^} (x–y)dx dy (f,g0) —:f×gf ^{^} ×g ^{^}(f,g 0) f^{^} g^{^} f g -, X — . , - f ₁f ₂ , f ₁ ^{^} ×gf ₂×g 0g. .     

Moduli of smoothness and best approximation in the spacesL p , 0<p<1

L ^p , 0<<1, .