By Conference on Harmonic Analysis and Partial Differential Equations (1988 : Florida Atlantic University), Tomas Schonbek

This e-book brings jointly ten papers offered on the convention on Harmonic research and Partial Differential Equations, held in April 1988 at Florida Atlantic college. The papers light up the connection among harmonic research and partial differential equations and current result of the various preferable specialists in those areas.Among the themes coated are: software of absolutely nonlinear, uniformly elliptic equations to the Monge Ampere equation; estimates for eco-friendly features for the aim of learning Dirichlet difficulties for operators in non-divergence shape; an extension of classical strength idea to the case of non gentle domain names; the relation among Riesz potentials and maximal fractional operators as a result of Muckenhoupt and Wheeden; and the Lax-Phillips scattering thought utilized to the double Hilbert rework. Directed at examine mathematicians and graduate scholars, the papers require wisdom of the classical instruments of research, similar to degree thought, Sobolev areas, and strength idea

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**Example text**

Lakl ~ ... be a decreasing rearrangement of the sequence (ak) of numbers. e. if and only if L L 00 p=O { lakf(log k)2 }1/2 < 00 . kElp The idea of studying unconditional convergence is due to Wladislaw Orlicz {12}, who proved the first basic result in this direction. His result , which is actually a consequence of the above theorem of Tandori, is formulated in terms of the so-called Weyl multiplier. 52 F. M6ricz Corollary. Let (A(k) : k = 1,2 , ... ) be an increasing sequence of positive numbers.

Orthogonal Series A 21f-periodic function I is said to satisfy the uniform Lipschitz condition of order a > 0, in symbol: I E Lip21r a, if Only the case 0 < a :S 1 is interesting: if a > 1, then w(f,o)/o tends to zero with o. Consequently, in this case f'(x) exists and is zero everywhere, and I is constant. The function w(f, 0), 0 :S 0 < 21f, is called the modulus of continuity of I. It is clear that a function I is uniformly continuous if and only if w(f, 0) tends to zero with o. On the other hand, I belongs to LiP21r 1 if and only if I is the antiderivative of a bounded function .

Tandori , tiber die Divergenz der Orthogonalreihen, Publicationes Math . Debrecen, 8 (1961), 291-307. {19} K. Tandori, tiber die orthogonalen Funktionen. II (Summation) , Acta Sci . Math . (Szeged), 18 (1957), 149-168 . {20} K. Tandori, tiber die orthogonalen Funktionen. X (Unbedingte Konvergenz) , Acta Sci . Math. (Szeged) , 23 (1962), 185-22l. {21} M. Zamansky, Classes de saturation de certains precedes d'approximation des series de Fourier, Annales de l'Ecole Normale Superieure, 66 (1949), 19-93 .