{'fraction_non_alphanumeric': 0.06443298969072164, 'fraction_numerical': 0.020618556701030927, 'mean_word_length': 4.256756756756757, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
On the moduli of continuity of Hp functions with 0

We prove two inequalities which relate the Lp modulus of continuity of n-th order, ωn(f,·)p, of an Hp function f with the p-th mean values of the n-th derivative f(n). Using these inequalities we extend classical results of Hardy and Littlewood [5], Gwiliam [4], Zygmund [13] and Taibleson [12] as well as a recent result of Oswald [6].