Integrability of multiple Walsh series and Parseval's formula

f(x,y) _jk . , {c _jk} , f(x, )(, ) [0,1)х[0,1) , - (0,0). , , f, - f. , , , [1] . . - [5] [6].

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This research is supported by National Science Council, Taipei, R.O.C. under Grant #NSC 84-2121-M-007-026.     

Differentiation of fractional order onp-groups,approximation properties

G- p- . [5] - (G) L _r(G) (1r<), . . , - . , , , . . , X. , . (. [1], [2] [4]).     

Arithmetic properties of the Markov function for the Jacobi weight

. . .     

On the uniform (C, 1)-summability of Fourier series and integrability of series with respect to multiplicative orthonormal systems

H (G), f(g)H (G) , (, 1)- OHMC G. , OHMC, A. H. . , . , OHMC, lim supp _n=, , ,n .. . , 117 234 . . -      

On a class of orthogonal series

, [0, 1], (n+1) n-. . [2]. — (. 5.4 5.6). . 6.4 2 [5]. , [4]. , , [6] [7]. [1].     

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

L ^p , 0<<1, .     

Onp-Helson sets in R n

p- . E R ⁿ -, f () _p(R ⁿ)., ER ⁿ 2nq ₀, E— - q ₀(q ₀-1). : q₀>2 n1 E R ⁿ 2nq ₀, p- p<₀. , f-[-, ]ⁿ, f A _p(R ⁿ) , _p([-, ]ⁿ) (1 << ).     

Produktsätze für Verfahren zur Limitierung von Doppelfolgen

{p _mn } - ₀₀>0, (1, 1) (1.1) (1.2). {s _mn } J _p - ( bJ _p -lims _mn =), (1.3) 0<x,y<1 p _s (, )/p(x, y) x, y 1-. {r _mn } - , (1.5) 0<, <1. N _rp - , (1.6). , bJ _p -lims _mn = bJ _q -lim(N _rps) _mn =. J _p - . , .     

О граничном поведени и неограниченных супергармонических функций

In this paper it is proved that a function, superharmonic on a domain inR ⁿ⁺¹ with Lipschitz boundary, cannot have nontangential limit equal to + on a set of positiven-dimensional measure on the boundary. As a corollary, a generalization of the uniqueness theorem of Lusin-Privalov on the nontangential limits of functions, analytic on a domain in the complex plane, is obtained for the case of functions, analytic on a domain in C ⁿ (n>1) with Lipschitz boundary. Formulation of a generalization of the main theorem is also given for the case of the solutions of uniformly elliptic equations with infinitely smooth coefficients.

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Waterman classes and spherical partial sums of double Fourier series

f(x,y) ₀BV(T²), ={1/n} _n=1 .

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Dedicated to Professor Károly Tandori, the outstanding mathematician and academician on his seventieth birthday

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This work was done under the financial support of the Russian Foundation for Fundamental Scientific Research, Grant 93-01-00240.     

On the convergence of Fourier series in the metric ofL 1

L ¹ .      

Orthogonal systems invariant under an automorphism

, , - ( ) . , - , ( ) .     

О решеткахИ-Радикалов, строгих слева Радикалов, наследственных слева радикалов

.     

On shifts of sequences

X ₂ ={x _k } _k=2 X={x _k } _k=1 . , , ( , ) . , , X— , , X ₂ H, , , , , X ₂ H.     

A note on rational approximation rate for Müntz system {x λn } with λ n ↘ 0

[Zho2] {x ⁿ } , _n 0 n .

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Supported in part by an NSERC Postdoctoral Fellowship and a CRF grant of University of Alberta.     

Convergence theorems for set-valued amarts and uniform amarts

( ) , — , - . .     

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.     

Embeddings of Lorentz—Marcinkiewicz spaces with mixed norms

X(Y) f -:X(Y)={fM(×): f_{X(Y)=f(x,.)YX<} . =(0, ), M (×) — , ×, X, Y, Z— . X(Y) Z(×).     

On the bestL p multipoint local approximation

P (f) — , f L ^p - , k . f 02k–2 P (f) 0.