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On the Divergence of the Two-Dimensional Dyadic Difference of Dyadic Integrals

✍ Scribed by G. Gát

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
204 KB
Volume
116
Category
Article
ISSN
0021-9045

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In this paper we prove the two-dimensional pointwise dyadic differentiability (provided that the distance of the indices is bounded) of the dyadic integral of integrable two-dimensional functions. We also prove some inequality of type (H, L 1 ) for the maximal operator sup n # N 2 |d n (If )|.

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## Abstract An approximation method for a wide class of two‐dimensional integral equations is proposed. The method is based on using a special function system. Orthonormality and good interaction with fundamental integral operators arising in partial differential equations are remarkable properties