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The dual of an inequality of Hardy and Littlewood and some related inequalities. (English) Zbl 0246.30031


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30D55 \(H^p\)-classes (MSC2000)
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[1] Flett, T. M., A note on some inequalities, (Proc. Glasgow Math. Assoc., 4 (1958)), 7-15 · Zbl 0136.04102
[2] Flett, T. M., Mean values of power series, Pacific J. Math., 25, 463-494 (1968) · Zbl 0162.10002
[3] Flett, T. M., Inequalities for the \(p\)-th mean values of harmonic and subharmonic functions with \(p\) ⩽ 1, (Proc. London Math. Soc., 20 (1970)), 249-275, (3) · Zbl 0217.10401
[4] Flett, T. M., A theorem concerning the real part of a power series, (Shankar, H., Mathematical essays dedicated to A. J. MacIntyre (1970)), 135-143, Ohio · Zbl 0211.09401
[5] Flett, T. M., On the rate of growth of mean values of holomorphic and harmonic functions, (Proc. London Math. Soc., 20 (1970)), 749-768, (3) · Zbl 0211.39203
[6] Flett, T. M., Temperatures, Bessel potentials and Lipschitz spaces, (Proc. London Math. Soc., 22 (1971)), 385-451, (3) · Zbl 0234.35032
[7] Gwilliam, A. E., On Lipschitz conditions, (Proc. London Math. Soc., 40 (1936)), 353-364, (2) · Zbl 0013.06803
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[10] Hardy, G. H.; Littlewood, J. E., A convergence criterion for Fourier series, Math. Z., 28, 612-634 (1928) · JFM 54.0301.03
[11] Hardy, G. H.; Littlewood, J. E., Some properties of conjugate functions, J. für Math., 167, 405-423 (1931) · Zbl 0003.20203
[12] Hardy, G. H.; Littlewood, J. E., Some properties of fractional integrals. II, Math. Z., 34, 403-439 (1932) · Zbl 0003.15601
[13] Hardy, G. H.; Littlewood, J. E., Theorems concerning mean values of analytic or harmonic functions, Quart. J. Math., 12, 221-256 (1941) · Zbl 0060.21702
[14] Littlewood, J. E., Lectures on the theory of functions (1944), Oxford · Zbl 0060.19906
[15] Mulholland, H. P., Some theorems on Dirichlet series with positive coefficients and related integrals, (Proc. London Math. Soc., 29 (1929)), 281-292, (2) · JFM 55.0202.02
[16] Taibleson, M. H., On the theory of Lipschitz spaces of distributions on Euclidean \(n\)-space. III. Smoothness and integrability of Fourier transforms, smoothness of convolution kernels, J. Math. Mech., 15, 973-981 (1966) · Zbl 0173.16103
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