On the convergence of double Fourier series of functions from Lp,p > 1 |
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Authors: | I L Bloshanskii |
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Institution: | 1. M. V. Lomonosov Moscow State University, USSR
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Abstract: | It is proved that if a function from Lp, p > 1, satisfies the condition $$\frac{1}{{t \cdot \tau }}\int_0^t {\int_0^\tau {\left| {f(x + u,y + v) - f(x,y)} \right|} dudv = O\left( {\left {1n\frac{1}{{(t^2 + \tau ^2 )}}} \right]^{ - 2} } \right),}$$ then the double Fourier series of function f, under summation over a rectangle, converges almost everywhere. |
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