请他们放心英文

Please set your heart at rest.或者Please disburden yourself.

You may rest assured.

叫别人放心，别怕： Dont worry,....叫别人放心，慢慢来： take it easy表示自己放心，你。。。。我就放心了，，，： be relax

Please trust us !Don't worry about it!

rest assured 放心；确信无疑be at ease 放心feel relieved 放心rest one's heart 叫某人放心！