In mathematics, the Hausdorff−Young inequality bounds the Lq-norm of the Fourier coefficients of a periodic function for q ≥ 2. William Henry Young () proved the inequality for some special values of q, and Hausdorff () proved it in general. More generally the inequality also applies to the Fourier transform of a function on a locally compact group, such as Rn. For Rn and gave a sharper form of it called the Babenko–Beckner inequality. We consider the Fourier operator, namely let T be the operator that takes a function on the unit circle and outputs the sequence of its Fourier coefficients

Earl Rashad Clark (born January 17, 1988) is an American professional basketball player who last played for San Pablo Burgos of the Liga ACB. He played college basketball for the University of Louisville and was drafted 14th overall by the Phoenix Suns in the 2009 NBA draft.

"Everything I Wanted" (stylized in all lowercase) is a song by American singer Billie Eilish. It was written by Billie Eilish and her brother Finneas O'Connell, with the latter handling production. The song was released as a single on November 13, 2019 through Darkroom and Interscope Records. It was described as a pop, electronica and indie pop track, for which a piano and downtempo bass provide minimalist instrumentation. Inspired by a nightmare she experienced, the song is about Eilish's strong relationship with her beloved brother Finneas. In the lyrics, Billie Eilish talks about him protecting her and making sure no one hurts her. "Everything I Wanted" received mainly positive reviews from music critics, several of whom praised the music and lyrics. Commercially, the song was also successful, reaching number eight on the US Billboard Hot 100. It debuted atop the record charts of several countries, including Ireland and Norway. The song further peaked at number three on the UK Singles Chart. It has been certified by several certifications, most notably double platinum in Australia, Canada, and the United States. Billie Eilish directed the accompanying music video, which was uploaded to her YouTube channel on January 23, 2020. The video depicts Billie Eilish and Finneas together, holding hands while driving through the city and into the ocean. Billie Eilish has performed "Everything I Wanted" live several times, with it being included on the setlist for her When We All Fall Asleep Tour (2019) and Where Do We Go? World Tour (2020).
"Everything I Wanted" (stylized in all lowercase) is a song by American singer Billie Eilish. It was written by Billie Eilish and her brother Finneas O'Connell, with the latter handling production. The song was released as a single on November 13, 2019 through Darkroom and Interscope Records. It was described as a pop, electronica and indie pop track, for which a piano and downtempo bass provide minimalist instrumentation. Inspired by a nightmare she experienced, the song is about Eilish's strong relationship with her beloved brother Finneas. In the lyrics, Billie Eilish talks about him protecting her and making sure no one hurts her.

In mathematics, the Hausdorff−Young inequality bounds the Lq-norm of the Fourier coefficients of a periodic function for q ≥ 2. William Henry Young () proved the inequality for some special values of q, and Hausdorff () proved it in general. More generally the inequality also applies to the Fourier transform of a function on a locally compact group, such as Rn. For Rn and gave a sharper form of it called the Babenko–Beckner inequality. We consider the Fourier operator, namely let T be the operator that takes a function on the unit circle and outputs the sequence of its Fourier coefficients Parseval's theorem shows that T is bounded from to with norm 1. On the other hand, clearly, so T is bounded from to with norm 1. Therefore we may invoke the Riesz–Thorin theorem to get, for any 1 < p < 2 that T, as an operator from to , is bounded with norm 1, where In a short formula, this says that This is the well known Hausdorff–Young inequality. For p > 2 the natural extrapolation of this inequality fails, and the fact that a function belongs to , does not give any additional information on the order of growth of its Fourier series beyond the fact that it is in .