{'fraction_non_alphanumeric': 0.08819345661450925, 'fraction_numerical': 0.03556187766714083, 'mean_word_length': 4.374045801526718, 'pattern_counts': {'":': 0, '<': 1, '<?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}}
A ON NONLINEAR NON-CONVOLUTION TYPE SINGULAR INTEGRAL OPERATORS

. In this paper, we present some general results on the pointwise convergence of the non-convolution type nonlinear singular integral operators in the following form: where Ψ = (cid:104) a, b (cid:105) and Ω = (cid:104) A, B (cid:105) stand for arbitrary closed, semi-closed or open bounded intervals in R or these set notations denote R , and Λ is a set of non-negative numbers, to the function f ∈ L p,w (Ω), where L p,w (Ω) denotes the space of all measurable functions f for which (cid:12)(cid:12)(cid:12) fw (cid:12)(cid:12)(cid:12) p (1 ≤ p < ∞ ) is integrable on Ω , and w : R → R + is a weight function satisfying some conditions.