Affine fractional $$L^p$$ Sobolev inequalities

Abstract

Sharp affine fractional $$L^p$$ L p Sobolev inequalities for functions on $${\mathbb {R}}^n$$ R n are established. The new inequalities are stronger than (and directly imply) the sharp fractional $$L^p$$ L p Sobolev inequalities. They are fractional versions of the affine $$L^p$$ L p Sobolev inequalities of Lutwak, Yang, and Zhang. In addition, affine fractional asymmetric $$L^p$$ L p Sobolev inequalities are established.

Investigating the Impact of Mindfulness Meditation on Stress Reduction and Self-Compassion of Nursing Health Care Professionals in a Small Community Hospital in the Midwest

“…Although nursing health care professionals make up a significant portion of health care workers, the nursing profession has endured concerns about shortage (due to baby boomers and retirement) and burnout (work-related stress) since the 1970s-with a growing concern during the COVID-19 pandemic. [10][11][12][13] In fact, the COVID-19 pandemic has exacerbated (exponentially) the concerns of work-related stress, burnout, intention to leave, and nursing staffing shortage. In 2020, the World Health Organization revealed there was a global shortage of nurses of approximately 5.9 million nurses.…”

“…In 2020, the World Health Organization revealed there was a global shortage of nurses of approximately 5.9 million nurses. [11][12][13] The International Council of Nurses suggests the pandemic could trigger a mass exodus from the profession in the near future and estimates the global nurse shortage could be widened to nearly 13 million in the aftermath of the pandemic crisis. 11 Nursing staff have endured high stress, and increased responsibilities due to the pandemic and staffing needs.…”

“…According to the National Nursing Workforce Survey,9 there are approximately 4.2 million registered nurses (RNs), approximately 950 000 licensed practical nurses/licensed vocational nurses (LPNs/LVNs), and approximately 325 000 nurse practitioners (NPs). Although nursing health care professionals make up a significant portion of health care workers, the nursing profession has endured concerns about shortage (due to baby boomers and retirement) and burnout (work-related stress) since the 1970s—with a growing concern during the COVID-19 pandemic 10–13. In fact, the COVID-19 pandemic has exacerbated (exponentially) the concerns of work-related stress, burnout, intention to leave, and nursing staffing shortage.…”

“…In fact, the COVID-19 pandemic has exacerbated (exponentially) the concerns of work-related stress, burnout, intention to leave, and nursing staffing shortage. In 2020, the World Health Organization revealed there was a global shortage of nurses of approximately 5.9 million nurses 11–13. The International Council of Nurses suggests the pandemic could trigger a mass exodus from the profession in the near future and estimates the global nurse shortage could be widened to nearly 13 million in the aftermath of the pandemic crisis 11.…”