On rearrangements of the Haar system in the space BMO

, .     

Fortsetzungssätze und Moduln über Semifields

. . — . — —.

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Herrn Professor Dr. Frank Terpe zum 60. Geburtstag gewidmet     

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

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On the equivalence of some rearrangements of the two-parameter Haar system

h ₁, L _p .

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

Some inequalities of Hardy-Littlewood type

[3] , >0 n ^– a _n , . , . . , .

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

A generalized Laplace transform of generalized functions

- . . . , .     

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).     

On summability of subsequences of partial sums of trigonometric Fourier series

n- (n1) fL ^p ([–, ] ⁿ ),=1 = (L C) . , , f([–, ] ⁿ ).     

Differentiation of fractional order onp-groups,approximation properties

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

On the bestL p multipoint local approximation

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

On multipliers in the spaces 207-01207-01207-01

. . , . , , , . , . .

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Finally, the author wishes to express his gratefulness to Prof. P. I. Lizorkin for raising the problem and for his attention during the elaboration of the present work.     

Investigation of Haar and Franklin series in Hardy spaces

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

On certain imbedding and extension theorems for a weighted class of functions

n- , S n–1 m (0m<n), () S . () , ().     

Идеологиыеское знаыение геометрии бояи—лобаыевского

... , , . ( ) , , . (. )     

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. .     

Martingale Hardy spaces,BMO and VMO spaces with nonlinearly ordered stochastic basis

VMO. , ⁺, «» VMO . « » .     

A generalized integral with applications to trigonometric series

, . . .

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The authors wish to thank the referee whose comments improved the presentation of the paper. In fact, the present form of Lemma 2, which was originally very long, is due to the referee.     

Saturation theorems for discretized linear operators

, , , - .

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Part of this research was completed at a conference of Hungarian and American mathematicians held in Madison, Wisconsin, August 1974, and sponsored by the National Science Foundation (USA) and the Institute for Cultural Relations (Hungary).

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The first author gratefully acknowledges NSF support in Grant GP 19620.     

Arithmetic properties of the Markov function for the Jacobi weight

. . .     

Convergence theorems for set-valued amarts and uniform amarts

( ) , — , - . .