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- W4307713421 abstract "Abstract In this paper, we introduce a family of one-dimensional maximal operators $mathscr{M}_{kappa ,m}$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>M</mml:mi> <mml:mrow> <mml:mi>κ</mml:mi> <mml:mo>,</mml:mo> <mml:mi>m</mml:mi> </mml:mrow> </mml:msub> </mml:math> , $kappa geq 0$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>κ</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>0</mml:mn> </mml:math> and $min mathbb{N}setminus {0}$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>m</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>N</mml:mi> <mml:mo>∖</mml:mo> <mml:mo>{</mml:mo> <mml:mn>0</mml:mn> <mml:mo>}</mml:mo> </mml:math> , which includes the Hardy–Littlewood maximal operator as a special case ( $kappa =0$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>κ</mml:mi> <mml:mo>=</mml:mo> <mml:mn>0</mml:mn> </mml:math> , $m=1$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>m</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> </mml:math> ). We establish the weak type $(1,1)$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mo>(</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>)</mml:mo> </mml:math> and the strong type $(p,p)$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mo>(</mml:mo> <mml:mi>p</mml:mi> <mml:mo>,</mml:mo> <mml:mi>p</mml:mi> <mml:mo>)</mml:mo> </mml:math> inequalities for $mathscr{M}_{kappa ,m}$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:msub> <mml:mi>M</mml:mi> <mml:mrow> <mml:mi>κ</mml:mi> <mml:mo>,</mml:mo> <mml:mi>m</mml:mi> </mml:mrow> </mml:msub> </mml:math> , $p>1$ <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML> <mml:mi>p</mml:mi> <mml:mo>></mml:mo> <mml:mn>1</mml:mn> </mml:math> . To do so, we prove a technical covering lemma for a finite collection of intervals." @default.
- W4307713421 created "2022-11-05" @default.
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- W4307713421 date "2022-10-28" @default.
- W4307713421 modified "2023-09-25" @default.
- W4307713421 title "Norm inequalities for maximal operators" @default.
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- W4307713421 doi "https://doi.org/10.1186/s13660-022-02874-1" @default.
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